Scotland fought back from two goals down to beat Poland in Kielce and keep alive their hopes of qualifying for the 2019 World Cup.
Dzesika Jaszek lobbed Poland into an early lead from a tight angle, and then Sophie Howard turned a cross into her own net to double the deficit.
Kim Little's free-kick evaded everyone to pull one back, then Jane Ross drilled a low shot into the corner.
Cuthbert and Little went close before Lisa Evans scored a 90th-minute winner.
Scotland remain three points behind Switzerland, who beat Albania 4-1 away from home, in Group Two, with Shelley Kerr's side facing the leaders at home in their next game in August.
The Scots are currently fifth best of the second-place sides - they need to be in the top four to net a play-off spot at least.
Scotland as a nation are good at hard luck stories. Snatching defeat from the jaws of victory. But this Scotland side produced a thrilling comeback just when it was needed.
The task was clear. Anything other than victory would most likely end any hope of automatic progression to France 2019.
However, in the opening minutes, goalkeeper Lee Alexander had possession but played it into an area that proved costly. Striker Jaszek gathered on the right and fired in a cross which sailed over Alexander's head straight into the net.
A quick, positive response was needed and Kerr's side did just that; dominating the ball, gaining territory and approaching Poland's penalty area with a fair degree of regularity.
Little squared for Cuthbert, but her shot from inside the area was blocked for a corner.
Set plays were too near the goalkeeper. Cross balls were too close to the goalkeeper. Direct efforts on goal were not forthcoming.
Kerr had pinpointed Poland's physicality and that was evident when Cuthbert was cleaned out three times in quick succession. Only one booking emerged to the frustration of the Scottish bench.
Fiona Brown volleyed over from a fabulous position. Cuthbert and Brown had opportunities from close range but could not get the shot away.
It needed a spark of creativity which came when Christie Murray slid Little in who may have struck first time but delayed allowing a challenge to come in. The ball was scrambled away.
That miss was quickly and cruelly punished and again it was a soft concession.
Howard looked in control as a ball flew in from the right, but she stretched and diverted the ball past Alexander for an agonising own goal.
Caroline Weir then had to scamper back to prevent a third with Agata Tarczynska about to pull the trigger.
There seemed no way back as the clock ticked on. Incredibly, there was.
Little floated in a free kick from the left which evaded everyone and found the corner to give Scotland hope.
Then captain Rachel Corsie released Evans who squared for substitute Ross to find the corner.
Alexander then saved superbly from a close range volley to keep Scotland in it. That was crucial to what happened next.
Superb interplay released Cuthbert whose shot deflected but onto the post and away.
Little then smashed from distance and watched in horror as the ball struck the bar, bounced down and out.
The drama continued. In the last minute, Evans beat a defender and found the far corner for a sensational winner, and Scotland now leave Poland on the ultimate high.
Line-ups
Poland
Formation 4-4-2
- 1Kiedrzynek
- 5Sikora
- 18Grad
- 7Gusciora
- 21Wiankowska
- 16Grabowska
- 14SiwinskaBooked at 40mins
- 17DaleszczykSubstituted forMatysikat 73'minutes
- 11KamczykSubstituted forTarczynskaat 58'minutes
- 15Winczo
- 6JaszekSubstituted forMatuschewskiat 58'minutes
Substitutes
- 2Pozerska
- 4Matysik
- 8Chudzik
- 10Tarczynska
- 12Szymanska
- 20Matuschewski
- 23Mesjasz
Scotland
Formation 4-2-3-1
- 1Alexander
- 15Howard
- 4Corsie
- 5Beattie
- 3Mitchell
- 16MurraySubstituted forRossat 68'minutes
- 9Weir
- 11Evans
- 8Little
- 20BrownSubstituted forArnotat 75'minutes
- 22Cuthbert
Substitutes
- 6Love
- 7Lauder
- 12Lynn
- 13Ross
- 14Arthur
- 19Clelland
- 23Arnot
- Referee:
- Stéphanie Frappart
- Attendance:
- 4,410