Arsenal appeared to be heading towards a shock defeat after Josh Murphy's clever finish in the 34th minute put the Championship side ahead at Emirates Stadium.
But Nketiah made a stunning contribution from the bench, scoring less than 60 seconds after his introduction for Reiss Nelson in the 85th minute to open his account for the senior team
Nketiah then secured Arsenal's passage in the sixth minute of extra time, leaving Wenger baffled by Chelsea's decision to let him leave their academy as a 14-year-old.
"I don't know what happened at Chelsea," Wenger told reporters. "He has scored goals at youth level and sometimes I don't know why they let him go.
"I don't know why. You see that more and more. Young people travel from one club to another. I don't know.
"He has top quality and is one of player who was with me in pre-season and I knew what he could do.
"I must say I am impressed when I think he was not even conceived when I was already here [became Arsenal manager].
"But it is good as well. Life gives a chance to young people and hopefully he will make a long career at Arsenal. We are proud to give young players a chance."