Roy Hodgson's men were given the lead thanks to Andy Carroll's thumping header, however a Glen Johnson own-goal and Olof Mellberg's effort put Sweden in the driving seat. The Arsenal winger was then introduced to the fray and proceeded to net an equaliser with a thunderous drive before assisting Welbeck's improvised winner.
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"That chance was massive, but Danny made it look easy," he told The Telegraph. "It was class, probably one of the best goals at this tournament and I am not just saying that because he's my friend.
"That goal had everything and shows that, despite being at such a young age he can do the business."
The Gunners' attacker came off the bench to score his first goal for England since bagging a hat-trick against Croatia in a World Cup qualifier four years ago.
The former Southampton player was delighted to find the back of the net once more, but admitted he was surprised that his effort beat the keeper.
"I have finally got that scoring monkey off my back, but I surprised myself," he continued. "I thought the shot took a deflection which is why my celebration was a little bit odd, but I've seen it again and it didn't.
"I didn't know I had that sort of 'Ronaldo dip' in me. I should try it more often. To score is special, not just for me but for my family watching back home."
Indeed Sweden midfielder Sebastian Larsson told Goal.com after the goal that he felt Walcott's goal was a fluke saying: "If he tries it a thousand times he won't score again, that's the truth."
England now face co-hosts Ukraine on Tuesday night in their final Group D game, needing just a point to secure progression to the knockout round. The team will also be boosted by Wayne Rooney's return from suspension, a player Walcott believes is too good to leave out.
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He added: "I am sure Wayne will get his opportunity. He'll want to make up for time he's missed – he will want to make it up to all of the lads.
"He is such a world-class player. It would be tough to leave him out but that's the manager's decision. We'll see what happens."
With Welbeck and Carroll both scoring against Erick Hamren's men, Hodgson faces a decision as to whether he brings the returning Red Devils forward straight back into the team, however, the 64-year-old insisted it is a good dilemma to be faced with and suggested the former Everton man will play aganst Oleg Blokhin's side.
"I welcome those kind of selection problems," Hodgson said. "I was really pleased with the performance of the front players, but Wayne Rooney is a special player and, frankly, it will be hard to leave him out."