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Celtic are "close" to completing a deal for Sead Haksabanovic, manager Ange Postecoglou confirmed, after his side overcame an awkward test against Hearts to move two points clear at the Scottish Premiership summit.
The hosts capitalised on Rangers' draw at Hibernian, with Kygo Furhashi netting the opener before Giorgos Giakoumakis' goal in the final seconds.
Hearts improved after the break, but had no shots on target and ended with nine men after second yellows for Alex Cochrane and Toby Sibbick late on.
Celtic maintained their perfect start with a fourth straight victory, and are set to bolster their squad with the signing of 23-year-old Montenegro winger Haksabanovic, who is seeking to leave Russian side Rubin Kazan.
"Yeah, I think that's a fair assessment - it's getting close," Postecoglou told Sky Sports of a potential deal.
Hearts, whose line-up reflected the importance of their looming Europa League play-off second leg with FC Zurich, lost for the first time in the league this season.
Craig Gordon, Barrie McKay and Lawrence Shankland were among the key players rested as Hearts boss Robbie Neilson made seven changes from the 2-1 first-leg defeat in Switzerland.
But even accounting for the upheaval, the visitors' defending was dire as they fell behind in the opening 15 minutes.
Kyogo was left all alone six yards out to volley past stand-in goalkeeper Ross Stewart after Daizen Maeda wriggled clear of Cochrane and whipped over a cross from the right.
Hearts regrouped and manfully prevented further damage before the break, with Jota lashing into the side-netting, Matt O'Riley knocking an acrobatic effort wide and Maeda wastefully planting a header into Stewart's arms from close range.
Hearts were too often hurried in possession, but cut Celtic open when neat interplay in midfield allowed Gary Mackay-Steven to spring Josh Ginnelly clear, only for the winger to drag wide.
The visitors' belief blossomed as Celtic started the second half in sloppy fashion. Ginnelly screwed another effort wide while Sibbick was unable to connect with Alan Forrest's tempting ball across the face of goal.
Yet Hearts were unable to trouble goalkeeper Joe Hart, even after throwing on McKay and Shankland for the final half hour.
Celtic's search for a second goal was thwarted by Stewart's fine save from O'Riley, with substitute Hatate bundling the rebound a foot past. But Giakoumakis finally found a way through when he bundled in Josip Juranovic's fizzed delivery.
Man of the match - Kyogo Furuhashi
Solid Celtic keep on rolling - analysis
While Celtic's flawless start continues, they made hard work of overcoming a patchwork Hearts side.
The hosts allowed slackness to seep into their play in the second half, with loose passes and careless possession giving their visitors a foothold.
Still, Celtic's defensive solidity saw them through the rocky patch, with a third clean sheet secured while restricting the visitors to a meagre XG (expected goals) of 0.15.
At the other end, Celtic created more than enough chances to make the game safe long before Giakoumakis' goal. Having come off the bench to net in successive games, has the Greece striker earned a start next weekend?
One look at the Hearts teamsheet showed Neilson's priorities this week clearly lie elsewhere, with the manager taking no risks on his main men amid various bumps and bruises.
The early concession could have opened the floodgates, but Hearts dug in impressively and knocked Celtic off their stride after the break.
However, they were bereft of cutting edge and their set-piece deliveries lacked quality as the Edinburgh men's plucky efforts came to nothing.
What did they say?
Celtic manager Ange Postecoglou: "It was a game where there was no real flow to it. It was very stop-start, hard to get real tempo. Some of it was our own doing.
"Through that, we still maintained control and even though it was 1-0 for a long time, I never felt threatened. Their keeper pulled off two or three good games to keep them in the game."
Hearts manager Robbie Neilson: "I was pleased with the players that came in. We don't have a big squad but we've got real quality in the depth of the squad.
"For large periods of the game we played well. Until the referee sends two of our players off, we're still in the game and we're in a good position."
What's next?
Hearts are banking on home advantage helping them turn the tie around when they face Swiss champions FC Zurich in the Europa League play-off second leg at Tynecastle on Thursday (20:00 BST).
They then host St Johnstone in the Premiership next Sunday (15:00), with Celtic away to Dundee United the same day (12:00).
Player of the match
FuruhashiKyogo Furuhashi
with an average of 7.61
Celtic
Squad number8Player nameFuruhashi
Squad number17Player nameJota
Squad number7Player nameGiakoumakis
Squad number20Player nameCarter-Vickers
Squad number3Player nameTaylor
Squad number42Player nameMcGregor
Squad number6Player nameJenz
Squad number41Player nameHatate
Squad number88Player nameJuranovic
Squad number33Player nameO'Riley
Squad number1Player nameHart
Squad number38Player nameMaeda
Squad number14Player nameTurnbull
Squad number11Player nameAbada
Squad number13Player nameMooy
Heart of Midlothian
Squad number13Player nameStewart
Squad number15Player nameRowles
Squad number30Player nameGinnelly
Squad number17Player nameForrest
Squad number5Player nameHaring
Squad number11Player nameMackay-Steven
Squad number16Player nameHalliday
Squad number19Player nameCochrane
Squad number18Player nameMcKay
Squad number9Player nameShankland
Squad number21Player nameSibbick
Squad number10Player nameBoyce
Squad number27Player nameSmith
Squad number20Player nameNeilson
Squad number2Player nameSmith
Squad number12Player nameAtkinson
Line-ups
Celtic
Formation 4-3-3
- 1Hart
- 88Juranovic
- 20Carter-Vickers
- 6Jenz
- 3Taylor
- 33O'RileySubstituted forMooyat 72'minutes
- 42McGregor
- 14TurnbullSubstituted forHatateat 56'minutes
- 38MaedaSubstituted forAbadaat 56'minutes
- 8FuruhashiSubstituted forGiakoumakisat 72'minutes
- 17Neves Filipe
Substitutes
- 4Starfelt
- 7Giakoumakis
- 11Abada
- 13Mooy
- 25Bernabei
- 31Siegrist
- 41Hatate
- 49Forrest
- 56Ralston
Hearts
Formation 4-2-3-1
- 13Stewart
- 12Atkinson
- 21SibbickBooked at 90mins
- 15Rowles
- 19CochraneBooked at 89mins
- 16HallidaySubstituted forSmithat 60'minutes
- 5HaringSubstituted forNeilsonat 71'minutes
- 17ForrestSubstituted forMcKayat 64'minutes
- 10BoyceBooked at 26minsSubstituted forShanklandat 65'minutesBooked at 83mins
- 11Mackay-StevenBooked at 43minsSubstituted forSmithat 71'minutes
- 30Ginnelly
Substitutes
- 2Smith
- 7Grant
- 9Shankland
- 14Devlin
- 18McKay
- 20Neilson
- 27Smith
- 39Pollock
- 40McFarlane
Referee:Kevin Clancy
Attendance:58,776
Live Text
Match ends, Celtic 2, Heart of Midlothian 0.
Second Half ends, Celtic 2, Heart of Midlothian 0.
Goal! Celtic 2, Heart of Midlothian 0. Giorgos Giakoumakis (Celtic) right footed shot from very close range to the bottom left corner. Assisted by Josip Juranovic with a cross.
Attempt blocked. Reo Hatate (Celtic) right footed shot from outside the box is blocked. Assisted by Greg Taylor.
Corner, Celtic. Conceded by Michael Smith.
Corner, Celtic. Conceded by Ross Stewart.
Attempt saved. Giorgos Giakoumakis (Celtic) left footed shot from the centre of the box is saved in the bottom right corner. Assisted by Reo Hatate.
Second yellow card to Toby Sibbick (Heart of Midlothian) for a bad foul.
Liel Abada (Celtic) wins a free kick in the attacking half.
Foul by Toby Sibbick (Heart of Midlothian).
Second yellow card to Alex Cochrane (Heart of Midlothian) for a bad foul.
Callum McGregor (Celtic) wins a free kick on the right wing.
Foul by Alex Cochrane (Heart of Midlothian).
Foul by Reo Hatate (Celtic).
Nathaniel Atkinson (Heart of Midlothian) wins a free kick on the right wing.
Lawrence Shankland (Heart of Midlothian) is shown the yellow card for a bad foul.
Greg Taylor (Celtic) wins a free kick in the defensive half.
Foul by Lawrence Shankland (Heart of Midlothian).
Foul by Greg Taylor (Celtic).
Connor Smith (Heart of Midlothian) wins a free kick in the defensive half.