Despite defending well in the first 45 minutes, Wales only briefly threatened when the game was well beyond them.
Gareth Southgate made four changes to the side that drew 0-0 with the United States in their last game, with Foden coming into the side, along with Rashford, Jordan Henderson and Kyle Walker, who was making his first appearance following a groin operation in October.
Wales coach Robert Page handed a start to Joe Allen, while Daniel James also returned to the side after starting on the bench against Iran.
The game quickly settled into a pattern with England in possession and happy to keep the ball, even if it meant a stream of horizontal and backwards passes, while Wales kept their shape, got everyone behind the ball and gave nothing away, but offered nothing in attack until Allen fired high and wide in injury time.
Harry Kane looked to spring England into life, winning the ball in the last third and slipping Rashford through on goal, but goalkeeper Danny Ward was out quickly to make a vital block.
Neco Williams had to go off with concussion after Rashford's powerful shot caught him on the head, with Connor Roberts on to replace him.
Only when Foden - exiled on the right - was able to move inside and link with Jude Bellingham did England up a gear, with a move involving the youngsters ending with Foden shooting just over in the 37th minute.
There was a surprise at halftime when Wales captain Gareth Bale was replaced by Brennan Johnson, although the veteran had been a peripheral figure at best.
England sealed the game in 98 seconds between the 50th and 51st minutes, with Foden a key figure, first winning a free kick that Rashford smashed past the wall and the helpless Ward.
The Manchester City youngster then added a second sliding home at the far post after Rashford dispossessed Ben Davies for Kane to send over an inviting low cross.
Wales tried to react, with James curling a shot just wide, and Jordan Pickford made a reflex save after Kieffer Moore's shot took a big deflection.
Southgate gave an opportunity to Trent Alexander-Arnold, Kalvin Phillips and Callum Wilson, before Rashford made it 3-0. The forward collected a long pass from Declan Rice, cut inside and sent in a low shot that skidded between Ward's legs.
It was the 100th goal England have scored in the World Cup finals since their first appearance in 1950 and a good end to a successful night.