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Wales need only a draw in their final Group I qualifier against Slovenia to secure a World Cup play-off place after a 1-0 win in Greece.
Teenager Carrie Jones' first international goal saw Wales claim victory in Volos.
They now return to Cardiff for a mouthwatering group finale on Tuesday.
Should Wales avoid defeat against Slovenia, their direct rivals, they will be in the World Cup play-offs for the first time.
Slovenia earlier beat winless Group I bottom team Kazakhstan 1-0 and, if they beat Wales, would climb above them into second place and leave Gemma Grainger's side rueing a missed opportunity.
It is a prospect Wales, who are set to be backed by a record crowd of more than 10,000 fans at the Cardiff City Stadium, will not want to contemplate having given themselves a golden chance to break new ground.
While there is still much work to do before they can start planning for a first major tournament appearance, they remain in the hunt having done little wrong so far in this qualifying campaign.
Their only defeats have come against runaway group winners France and they began as firm favourites to win in Greece, having thrashed the same opposition 5-0 on a freezing night in Llanelli last November.
The conditions were very different in Volos, with thunder and lightning over the Panthessaliko Stadium in the late summer Greek heat, but that did not stop Wales taking control once more.
The visitors settled after a scrappy opening spell, dominating possession as well as territory as Greece sat deep.
Ceri Holland had Wales' first sighter, a header from Rhiannon Roberts' cross which looped over the bar, before the Liverpool midfielder's alertness almost brought the opening goal.
Holland picked off a stray Greek pass and burst into the penalty area, drawing a fine diving save from Zoi Nasi with a shot destined for the far corner.
From the corner which followed, Natasha Harding's cross-shot flew dangerously across the face of the Greek goal, before another set-piece saw Wales go in front in the 34th minute.
Rachel Rowe drilled a free-kick from near halfway into the penalty area, where Gemma Evans flicked on for 18-year-old Jones.
Though her initial effort was blocked, the Leicester City midfielder - on loan from Manchester United - made no mistake at the second attempt, driving the ball home from eight yards despite Nasi's efforts.
Having worked hard for their lead, Wales almost gave it away inside two minutes as Eleni Markou burst forward only for Laura O'Sullivan to make a vital save.
Greece showed more attacking intent in the second period, though it was Wales who came close when Jones was picked out by Hayley Ladd. This time she was denied by Nasi.
Jones next embarked on a sparkling run which ended with Angharad James taking aim from 20 yards, but once more Nasi was on hand to save.
Wales' failure to stretch their lead meant there was tension until the end, with Rowe making an important block when the ball dropped invitingly for Vasiliki Giannaka.
With that, Wales' work for the night was done - now to finish the job on Tuesday.
Line-ups
Greece
Formation 3-4-3
- 12Nassi
- 23Palama
- 8SidiraSubstituted forGeorgiouat 69'minutes
- 16NefrouBooked at 42mins
- 2Giannaka
- 7Kakambouki
- 17Moraitou
- 3Mitkou
- 21KoggouliSubstituted forSpyridonidouat 76'minutes
- 9Markou
- 10SarriSubstituted forChatzinikolaouat 81'minutes
Substitutes
- 1Giannakouli
- 4Kiamou
- 5Kapnisi
- 6Georgiou
- 11Spyridonidou
- 13Papakonstantinou
- 14Chatzinikolaou
- 15Goula
- 18Pouliou
- 19Georgantzi
- 20Pitsiou
- 22Paterna
Wales
Formation 4-4-1-1
- 1O'Sullivan
- 5Roberts
- 14Ladd
- 3Evans
- 13RoweBooked at 37mins
- 11Harding
- 8JamesBooked at 90mins
- 4Ingle
- 20Jones
- 18Holland
- 9GreenSubstituted forWardat 90+6'minutes
Substitutes
- 2Woodham
- 6Green
- 7Ward
- 10Fishlock
- 12Clark
- 15Hughes
- 16Estcourt
- 17Walters
- 19Wynne
- 21Middleton-Patel
- 22Filbey
- 23Morgan
Live Text
Match ends, Greece Women 0, Wales Women 1.
Second Half ends, Greece Women 0, Wales Women 1.
Foul by Ceri Holland (Wales Women).
Maria Mitkou (Greece Women) wins a free kick in the defensive half.
Offside, Wales Women. Angharad James tries a through ball, but Carrie Jones is caught offside.
Substitution, Wales Women. Helen Ward replaces Kayleigh Green.
Angharad James (Wales Women) is shown the yellow card.
Carrie Jones (Wales Women) wins a free kick on the left wing.
Foul by Maria Palama (Greece Women).
Corner, Wales Women. Conceded by Maria Mitkou.
Offside, Wales Women. Angharad James tries a through ball, but Kayleigh Green is caught offside.
Attempt saved. Rachel Rowe (Wales Women) right footed shot from a difficult angle and long range on the left is saved in the centre of the goal. Assisted by Carrie Jones.
Attempt blocked. Natasha Harding (Wales Women) right footed shot from the left side of the box is blocked. Assisted by Rachel Rowe.
Attempt saved. Eleni Markou (Greece Women) header from the centre of the box is saved in the centre of the goal. Assisted by Maria Mitkou.
Substitution, Greece Women. Despoina Chatzinikolaou replaces Veatriki Sarri.
Foul by Hayley Ladd (Wales Women).
Eleni Markou (Greece Women) wins a free kick in the attacking half.
Substitution, Greece Women. Anastasia Spyridonidou replaces Sophia Koggouli.
Foul by Carrie Jones (Wales Women).
Tatiana Georgiou (Greece Women) wins a free kick on the right wing.