The Welsh-based have found the rhythm after Carlos Carvalhal was appointed and are currently on nine matches unbeaten.
Korea Sung-Yeung’s lone strike condemned Burnley to a defeat, making it their fifth consecutive at the Liberty Stadium on Saturday.
And Ayew, who came off the bench against the Clarets for his first appearance since rejoining the club from West Ham United, has implored his team-mates to keep the momentum in their subsequent games until the end of the campaign
“The whole team is doing really well,” the forward said.
“We’re showing a lot of character and determination.
“We had a few chances in the first half, but we didn’t get nervous and kept playing our game. At the end of the day, we got the goal.
“It’s been a difficult period for us. We may have won but there are still a lot of games to go, so we just need to keep our momentum going as we’ve got a big game coming up against Brighton.”
Swansea City will face Sheffield Wednesday in the 5th Round of the Emirates FA Cup on Saturday.