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Rangers' remain top of the Scottish Premiership thanks to their first win at Dundee in five years, earned after Jason Cummings missed a penalty.
Joe Aribo's second goal of the season separated the sides at the break, following a half in which the hosts passed up a number of opportunities.
And Dundee extended their run to five games without a goal after Cummings' second-half spot kick was saved.
It leaves James McPake's side bottom, still searching for a first league win.
And his frustration was evident at full-time as he was red carded by Bobby Madden after protesting to the officials on the pitch.
Rangers, though, stay ahead of Hearts at the summit after breaking a run of two defeats and a draw in their previous visits to Dens, as well as a defeat further down the street against United earlier this season.
A lot of eyes were on Dundee striker Leigh Griffiths after he was charged by Police Scotland in relation to "culpable and reckless" conduct after apparently kicking a flare into a stand of fans during the midweek League Cup defeat to St Johnstone.
Added to being on loan from Celtic, the striker's desperation to score was clear. Twice in the opening minutes he spurned good opportunities with headers from close range.
Two more would come his way. A thumping volley towards the near post and a left-foot shot from inside the box, but both times goalkeeper Jon McLaughlin got himself behind the efforts.
And a frustrating day was to get worse for Griffiths, who limped off before half-time with an ankle injury.
His were not the only big chances that came Dundee's way as they looked to end a run of four games without a goal - Jordan McGhee headed straight at McLaughlin from six yards out.
However, as so often happens in these games, the underdogs were punished for not taking their chances as Aribo soon put the champions ahead.
James Tavernier found Alfredo Morelos, who knocked a delightful ball into Aribo's path and he finished coolly past Adam Legzdins.
Rangers had been - and continued to be - unusually quiet, but did threatening a second at times. Kemar Roofe forced a save from Legzdins, and Connor Goldson found his route to goal blocked by his own team-mate Morelos.
Dundee were testing the visitors from set-pieces and Ryan Sweeney's header was on target, but Rangers began to gain more control with John Lundstram forcing a save and Morelos firing wide from six yards out.
That was until Dundee were awarded a penalty after Paul McMullan was caught by the leg of McLaughlin - who was booked - and the home side had a golden opportunity to end their barren run in front of goal.
However, Cummings' effort down the centre of goal cannoned off the goalkeeper's foot and he was beaten to the rebound to as McLaughlin punched clear.
Still the home side had chances with McGhee steering a header the wrong side of a post, but their poor run in front of goal continues and they remain rooted to the bottom of the table.
Man of the match - Joe Aribo
What did we learn?
Dundee could not have done much more to put an end to their poor run in front of goal, but it's now five games without scoring for the Premiership's bottom club and they've yet to win a game in seven league matches.
Rangers at times showed the frailties which has concerned supporters this season, especially from set pieces with the home side causing numerous problems, but they're still top of the league and into the semi-final of the League Cup.
What's next?
Rangers are away to Sparta Prague in the Europa League on Thursday (17:45 BST), before hosting Hibernian in the Scottish Premiership on Sunday (15:00). Dundee are next in action on Saturday away to St Johnstone (15:00 BST).
Player of the match
SakalaFashion Sakala
with an average of 5.84
Dundee
Squad number1Player nameLegzdins
Squad number5Player nameSweeney
Squad number14Player nameAshcroft
Squad number3Player nameMarshall
Squad number4Player nameFontaine
Squad number24Player nameAnderson
Squad number8Player nameByrne
Squad number18Player nameMcMullan
Squad number6Player nameMcGhee
Squad number2Player nameKerr
Squad number35Player nameCummings
Squad number29Player nameGriffiths
Squad number10Player nameMcGowan
Squad number7Player nameJakubiak
Rangers
Squad number30Player nameSakala
Squad number22Player nameBacuna
Squad number23Player nameWright
Squad number33Player nameMcLaughlin
Squad number3Player nameBassey
Squad number2Player nameTavernier
Squad number6Player nameGoldson
Squad number20Player nameMorelos
Squad number26Player nameBalogun
Squad number17Player nameAribo
Squad number25Player nameRoofe
Squad number18Player nameKamara
Squad number7Player nameHagi
Squad number4Player nameLundstram
Line-ups
Dundee
Formation 3-5-2
- 1Legzdins
- 14Ashcroft
- 4Fontaine
- 5Sweeney
- 2Kerr
- 24AndersonSubstituted forMcGowanat 62'minutes
- 8ByrneSubstituted forJakubiakat 74'minutes
- 6McGhee
- 3MarshallBooked at 53mins
- 18McMullan
- 29GriffithsSubstituted forCummingsat 39'minutes
Substitutes
- 7Jakubiak
- 10McGowan
- 17McCowan
- 20Panter
- 21Lawlor
- 23Sheridan
- 35Cummings
Rangers
Formation 4-3-1-2
- 33McLaughlinBooked at 59mins
- 2Tavernier
- 6Goldson
- 26Balogun
- 3Bassey
- 18Kamara
- 4Lundstram
- 7HagiSubstituted forWrightat 73'minutes
- 17AriboBooked at 90mins
- 20MorelosSubstituted forSakalaat 67'minutes
- 25RoofeSubstituted forBacunaat 82'minutesBooked at 90mins
Substitutes
- 1McGregor
- 10Davis
- 16Patterson
- 22Bacuna
- 23Wright
- 30Sakala
- 31Barisic
Referee:Bobby Madden
Attendance:8,574
Live Text
Match ends, Dundee 0, Rangers 1.
Second Half ends, Dundee 0, Rangers 1.
Attempt missed. Scott Wright (Rangers) right footed shot from the centre of the box misses to the right.
Attempt blocked. Scott Wright (Rangers) right footed shot from the centre of the box is blocked. Assisted by Juninho Bacuna.
Juninho Bacuna (Rangers) is shown the yellow card.
Foul by Juninho Bacuna (Rangers).
Cammy Kerr (Dundee) wins a free kick in the defensive half.
Joe Aribo (Rangers) is shown the yellow card.
Corner, Rangers. Conceded by Cammy Kerr.
Attempt missed. Juninho Bacuna (Rangers) right footed shot from outside the box is close, but misses to the left.
Corner, Rangers. Conceded by Paul McGowan.
Calvin Bassey (Rangers) wins a free kick on the left wing.
Foul by Cammy Kerr (Dundee).
Jon McLaughlin (Rangers) wins a free kick in the defensive half.
Foul by Lee Ashcroft (Dundee).
Corner, Dundee. Conceded by James Tavernier.
Foul by Glen Kamara (Rangers).
Paul McGowan (Dundee) wins a free kick in the defensive half.
Substitution, Rangers. Juninho Bacuna replaces Kemar Roofe.
Corner, Dundee. Conceded by Joe Aribo.
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