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.
WH doctor: Trump requested cognitive exam
Last week, Mr Trump underwent a three-hour examination in his first medical check-up since becoming United States president. Trump last revealed details about his health two months before the November 2016 election, when he appeared on the "Dr.
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.
YouTube Introduces Tighter Requirements For Video Monetization Following Logan Paul Controversy
Those affected are likely to be those making less than $100 on the program each year. YouTube points it out as if to make the point that noone is really affected.