Chelsea started off the brighter of the two sides and, after Pedro had a goal ruled out for offside, Eden Hazad put his side ahead.
But the tie was turned on it’s head when Nacho Monreal’s effort deflected in off Antonio Rudiger with Granit Xhaka scoring the eventual winner in the second half.
It means Arsene Wenger remains on track to win the only domestic trophy that has alluded him throughout his time at Arsenal.
They will first have to get past a rampant Manchester City side, who beat Bristol City in their semi-final yesterday.
Wilshere has enjoyed a prolonged spell in Arsenal’s starting line-up since December and was once again instrumental in the win over Chelsea.
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And the 26-year-old credited the team as a whole for holding strong when Chelsea threw everything they had at Arsenal to try and score an equaliser.
“The team effort in the second half was key when we knew he had to dig deep,” Wilshere said.
“We might have got a formation wrong in the first 25 minutes and they have good players in the middle who could take advantage.
“At this level, we are creating a few more chances and it takes a bit of luck some time. We have to be up for it and ready to go.
“I wouldn’t see it as surreal being back here and in the first team.
“I went away on loan last season, but wanted to come back and fight for my place in the team.”