Welbeck scored a last-gasp winner on his first league appearance since last April to cut 10-man Leicester’s lead at the top to just two points.
“In the last two training sessions he was very strong and I decided in the end to include him in the squad,” said Wenger.
“It was a great decision.
“Everybody is extremely happy for him, because he has been out for 10 months, that is an eternity for a player.”
After scoring in the fifth minute of added time Welbeck threw himself into the crowd to celebrate wildly.
“It has been a bit of a rollercoaster for me missing a lot of football.
“It’s the first time in my career I’ve missed so much football. My family and friends know what I’ve been through and to get that winning goal is a beautiful feeling.”
Jamie Vardy put the visitors ahead with a first half penalty before the game turned in the 54th minute when Danny Simpson was sent off for two yellow cards in the space of five minutes.
Walcott equalised in the 70th minute before Welbeck stole the points.
Relieved boss Wenger said: “For a while, I thought eight points would be too much,” he said.
“A loss today would have been massive. Even after that you get all the negative vibes, the belief goes down, it would have been much more difficult.
“We would not have given up, but eight points is three games to come back. We would need to win three, they would need to lose three.”
Leicester boss Claudio Ranieri was upset with referee Martin Atkinson over Simpson’s bookings for fouls on Alexis Sanchez and Olivier Giroud.
“I am very angry because I think maybe I make mistakes but an international referee gives two yellow cards for normal fouls,” he said. “He was a little severe with us.
“Maybe because the crowd pushed a lot and put him under pressure.
“Also there were four minutes extra-time and there was five minutes extra-time when they scored.”
Ranieri’s men have been promised a holiday in Las Vegas if they win the title.
But for now have been given a week off to recharge.
“They go, I don’t know where, Dubai maybe,” said Ranieri. “They go wherever they want. I’m one day in London, then I go to Rome.”
