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.
Kyrgios fined for colourful language at Open
Jo-Wilfried Tsonga is coming off a five sets win over Denis Shapovalov that took 50 games to decide. Barring the occasional signs of annoyance, Kyrgios was largely subdued on court.
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.
Metal Gear Survive Open Beta Available Now On Xbox One
As you can see, it's possible to purchase supply boosters, AI companions, and more using your SV coins. Claiming that Metal Gear Survive has a lot working against it is a bold understatement.
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.
Strong quarter for Costa owner despite "tougher" conditions
This contrasts with a boom in the number of visitors to the United Kingdom , especially the capital, after the referendum. Whitbread blamed weak sales growth at Costa on falling numbers of people visiting UK High Streets.