Ayew opened the scoring against the Championship leaders, weaving his way through the away defence for a goal reminiscent of Ricky Villa's strike for Tottenham in the 1981 final replay.
However, parity lasted just three minutes before Swansea regained their lead, and there was no way back for Wolves as they crashed out in the third round to bring an end to their 14-match unbeaten streak across all competitions.
Speaking after the game, Carvalhal said: "We have now played five games and had two wins, two draws and one defeat against Tottenham, when we could have achieved something completely different", said the Swans manager.
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Ayew, who is in the best form of his Swans career, was a threat from the start, and nearly took advantage in the first few minutes after Wolves centre-back Kortney Hause slipped outside his own area.
Wolves did not get forward a lot in the first half, but the Swans did need good blocks from Alfie Mawson and Federico Fernandez to deny Alfred N'Diaye and Bright Enobakhare respectively. "When he scores a goal like that, I'm very happy about him".
"It was a great goal from Jordan and he deserves it". He is a fighter and works very hard for the team.
It worked immediately as the Portuguese made it 1-1, capitalising on Kristoffer Nordfeldt's failure to come off his line and clear the danger.
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Under current law, grocery, drug and convenience stores aren't allowed to sell cold beer but liquor stores are. A House committee voted 12-1 in favor of a proposal to lift the ban on Sunday alcohol sales.
The Liberty Stadium outfit visit Notts County for their next Cup fixture on January 27.
My team are reacting to what we are doing and we have had a good series of five games.
"We drew the second half and had all the momentum, but once again we were behind on the scoreline".
Defender Danny Batth will return to the Wanderers squad following suspension, but Ruben Vinagre is banned after being sent off in the first game between the two sides. We are building a team.
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Bon Jovi also addressed the elephant in the room: whether estranged guitarist Richie Sambora would be on hand for the induction. Bon Jovi has been a guest on the Stern Show for decades and said he knew it had to be Stern to hold the induction honors.