The victory meant the Swans picked up their 31st point of the season, two points behind Hull City who are in 17th spot.
It was Ayew’s fifth start in 10 appearances for manager Paul Clement’s team and he made it count with his second assist since moving from Aston Villa on transfer deadline day in January.
Fernando Llorente scored the opener early on 10 minutes with an assist by Gylfi Sigurdsson but the hosts had to work hard to keep the Potters at bay.
Jordan then turned provider on 70 minutes when he sent a pass into the path of Tommy Carroll and the midfielder pulled a long shot from outside of the box to beat Stoke goalkeeper Jack Butland.
He had a pass accuracy of 81.3 per cent as well as two shots and was ranked the fourth most impactful player on the team.
With four matches left in the season, Swansea need as many points as possible in order to avoid relegation.
But they will face a difficult run-in where they travel to Manchester United and Sunderland but will host Everton and end the campaign at home to West Bromwich Albion.