The 30-year-old forward has been delivering impressive performances for the Swans since the start of the 2020-21 campaign.
The Ghana international opened his season account against Wycombe Wanderers and also provided an assist in the encounter to ensure his side secured all three points last time out.
Following the eye-catching display, the versatile forward was handed his fourth start of the season at the Liberty Stadium and made the most of the opportunity.
Both sides missed several scoring chances as they went into the break without finding the back of the net.
The second half, however, saw more goal-mouth action and Millwall broke the deadlock through Jake Bidwell after he was set up by Morgan Gibbs-White in the 46th minute.
Tom Bradshaw levelled proceedings for Steve Cooper’s men five minutes later after benefitting from Shaun Hutchinson’s assist.
Ben Cabango then scored the all-important winning goal for Swansea in the 68th minute, firing home from close range.
Ayew, who featured for the duration of the game, made four key passes, had 55 touches in the encounter.
The forward will hope to help Swansea continue their impressive start to the season when they take on Huddersfield Town in their next league game on October 17.
Ayew teamed up with the Liberty Stadium outfit in January 2018 for his second spell and has featured in more than 55 league games for the side despite spending the 2018-19 season on loan with Fenerbahce.
The forward is currently Ghana national team captain and has more than 80 appearances for the West Africans.