Leicester took the lead when Jamie Vardy dispatched his penalty on the stroke of half-time after being brought down by Nacho Monreal in the box.
The visitors were reduced to 10 men when Danny Simpson was shown a second yellow card in the 54th minute.
Arsenal drew level when substitute Theo Walcott finished from close range, and Welbeck netted the winner when his glancing header from Mesut Ozil’s free-kick crept past Kasper Schmeichel deep into stoppage time.
Speaking on Sky Sports after the final whistle, Henry said: “I don’t actually know what to say. I’m happy for Danny, they left it late.
“What a way to come back and now their title chance is back on track.”
He added: “The ending was just like a great movie. Arsenal didn’t do enough to win the game at the end of the day, I thought.
“Leicester obviously went down to 10 men which made it easier for Arsenal to play – and what a finish!
“I’m very happy for Danny Welbeck because I see him every day in training and he’s suffered a lot not being able to help the team, and he helped the team massively.”
The result left Arsenal, who have not won the title since the 2003-04 campaign, second in the table and two points behind the leaders heading into the final 12 games of the season.
Arsenal’s next Premier League game is a trip to Manchester United on Sunday 28 February.
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