The Premier League champions' unexpectedly poor half was followed by a predictably strong second-half response.
Per Mertesacker hardly had the ideal preparation for the FA Cup final.
Victory was rich vindication for Wenger, whose Arsenal future is due to be decided by a board meeting in the coming days, and allowed him to salvage something from the most hard season of his 21-year tenure. But Conte's failure to make the right selection and get his tactics right may hint at the challenge he will face next season.
Arsenal sealed their win when Ramsey headed in from 12 yards, before Ospina made a point-blank save to deny Costa late on.
Newsmen report that Wenger had previously admitted that Arsenal's season was affected by the uncertainty around his position, as well as the protests calling for him to leave.
Persuading him to stay, maybe against his will, will be a tough challenge, but Arsenal are a big club and now is the time to act like one.
Arsenal even had the luxury of a man advantage from the 68th when Victor Moses received a second yellow card for diving.
Chelsea, which will be making its seventh FA Cup final appearance since 2000, is favored to win its eighth FA Cup trophy.
"The behaviour of some people during the season, that is what hurts me most".