A goal down to Wales at halftime after Gareth Bale struck a wonderful free kick from 30 metres, England manager Roy Hodgson brought on forwards Sturridge and Jamie Vardy, whom many fans had wanted to see start the game, to replace the ineffectual Raheem Sterling and Harry Kane.
It turned out to be a pivotal change as Vardy, England's Footballer-of-the-Year in the Premier League this season for his goalscoring at champions Leicester City, grabbed an equaliser in the 56th minute.
Then, with England piling on the pressure in the dying seconds, Sturridge scrambled his way through the box to fire home the winner from close range.
The result left England at the top of Group B on four points, ahead of Wales and Slovakia on three and Russia bottom with just one point.
"It's a great feeling, unbelievable," Sturridge said. "I'm grateful for the opportunity. It's only one more game in the group so no-one should get too excited. But it was an amazing feeling. It's great to help the boys win the game."
Wales would have won the group with victory, but instead they will meet Russia in their final game with their destiny still very much in their own hands.
"Obviously, we're massively disappointed but I'm proud of everyone. Inside, we still feel strong, we still feel happy," said Wales goalscorer Bale.
"We're enjoying it and the tournament's not over yet. We're still in the thick of it. We'll keep fighting all the way to qualify, and the fans have been amazing once again."
All talk of the recent fan violence in Marseille and Lille dissipated as the game kicked off amid a cacophony of noise and singing from both sets of fans.
England dominated most of the first half and Sterling could have put them ahead as early as the seventh minute, but he skied the ball over the bar from close range, and it did not get any better from there on for the Manchester City winger.
With Wayne Rooney dropping deep to pull the strings in midfield, England sought to make the most of the space behind the Welsh full backs, but their final ball into the box was often a poor one.
They went behind just before halftime when Rooney clattered into Hal Robson-Kanu, with Bale driving a dipping free kick over the England wall and past keeper Joe Hart, who perhaps should have done better having got a hand to the ball.
The jubilant Wales fans spent the break bouncing a beach ball around behind the goal, but the appearance of Vardy and Sturridge soon put a stop to their merriment.
Eleven minutes after coming on, the pair combined to draw England level. Sturridge lifted the ball into the box where it came off the head of Wales captain Ashley Williams, and Vardy pounced to score.
England continued to apply relentless pressure but were held at bay until deep into stoppage time.
Sturridge charged into the box, took a ball from Dele Alli, wriggled past one challenge and held off another before beating Wales keeper Wayne Hennessey with a powerful finish, conjured from little backlift.
"Everyone wants to be part of the playing lineup and coming off the bench you want to try to make an impact," Vardy said.
Wales captain Ashley Williams remained upbeat, despite the outcome.
"It's tough for everyone but we've got another game on Monday, so we won't get down about it," he said.
(Reporting by Philip O'Connor; Editing by Adrian Warner/Toby Davis)
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