Victory set up England’s last-16 clash with Group A runners-up Senegal on Sunday, while Wales crashed out in Qatar without a win for the first time at a major tournament.
Foden started at the Ahmad bin Ali Stadium after being left out of the goalless draw with the United States on Friday, winning a free-kick for Rashford to break the deadlock in the 50th minute.
Manchester City star Foden extended the lead just a minute later before Rashford doubled his tally to knock a lackluster Wales out of Group B, in which the USA beat Iran to advance as runners-up.
Rashford spurned a famous opportunity in the ninth minute after being denied by the running back Danny Ward, who replaced the suspended Wayne Hennessey.
England continued to dominate possession without testing Ward often as Foden fired over on the turn while Joe Allen pounced on a rare Wales chance off target before the break.
A masterful drive from Foden ended with England’s free-kick in a tempting position before Rashford whipped into the top right corner to beat the blindside Ward.
Harry Kane drilled across the area from the right soon after for Foden to convert at the back post before Jordan Pickford parried Kieffer Moore to keep Wales at bay.
Ward was again beaten with some ease when Rashford shot through the legs of the keeper to deny Jude Bellingham to keep the scores level late on.
What does it mean? England continue to dominate Wales to book the last 16 berth
The pressure was mounting on England after an underwhelming display in the stalemate in the USA, but Southgate’s side responded well in their first World Cup meeting with their British counterpart.
England remained patient throughout and reaped the rewards in a fast-paced second-half start to secure a seventh straight victory over Wales, scoring 14 and conceding just once in the round.
Knock-out football is where England have impressed in recent years and Southgate will know it’s time to prove something again as Wales return home after disappointing in their second appearance at the tournament.
1. Wales (4-2-3-1)
GK: Danny Ward – 4/10 – Good save from Rashford in the first half. Might have done a little better with the first and third goals.
RB: Neco Williams – 4/10 – Blocked a shot with his head and had to go off afterwards. Was all he did, but at least it was something.
CB: Joe Rodon – 3/10 – Won a few key headers, but that was all he could do.
CB: Chris Mepham -2/10 – Bit of a weak link at the heart of the Wales defence.
LB: Ben Davies – 4/10 – One of Wales’ better players.
CM: Ethan Ampadu – 3/10 – Swamped and dominated in the midfield.
CM: Joe Allen – 3/10 – Good to see him getting a World Cup start after injury, but was dominated in midfield.
RW: Gareth Bale – 1/10 – Probably injured, but not remotely involved in the game either way.
AM: Aaron Ramsey – 4/10 – The pick of the Welsh midfield, but that didn’t really say much.
LM: Dan James – 2/10 – Brought in for his pace and was probably gutted when Kyle Walker turned up.
CF: Kieffer Moore – 2/10 – Completely negated by poor service and the England centre backs.
SUB: Connor Roberts (36′ for Williams) – 3/10 – He did okay, comparatively speaking.
SUB: Brennan Johnson (45′ for Bale) – 4/10 – Didn’t get many opportunities on the ball but was at least brave on the occasions he did.
SUB: Harry Wilson (’77 for James) – N/A
SUB: Rubin Colwill (81′ for Allen) – N/A
Manager: Rob Page – 2/10 – Probably never had the tools to achieve what was needed, but didn’t even make a good fist of it.
2. England (4-2-3-1)
GK: Jordan Pickford – 6/10 – Did what was needed, which was a decent save in the second half.
RB: Kyle Walker – 6/10 – Not tested but looked sharp nonetheless.
CB: John Stones – 6/10 – Ditto really. Solid. Didn’t need to be spectacular.
CB: Harry Maguire – 6/10 – Highly amusing shot in the first half but decent showing from the Man Utd man.
LB: Luke Shaw – 6/10 – As solid as he needed to be.
CM: Declan Rice – 6/10 – Not tested defensively and not really needed offensively.
CM: Jordan Henderson – 7/10 – Probably a good game for him to play. Up for the battle from the first minute. Very vocal leader on the pitch.
RW: Phil Foden – 7/10 – Justified the clamour to get him in the side.
AM: Jude Bellingham – 6/10 – Influential, just quietly so.
LW: Marcus Rashford – 9/10 – A real thorn in the Welsh side. Scored two and could have had more.
CF: Harry Kane – 7/10 – Short of his best but created a great chance for Rashford and put a goal on a plate for Foden.
SUB: Callum Wilson (58′ for Kane) – 6/10
SUB: Kalvin Phillips (58′ for Rice) – 6/10
SUB: Trent Alexander-Arnold (58′ for Walker) – 6/10
SUB: Kieran Tripper (65′ for Shaw) – 6/10
SUB: Jack Grealish (76′ for Rashford) – N/A
Manager: Gareth Southgate – 8/10 – Easily criticised, but he got the big calls right (in this one). His decision to switch Rashford and Foden after the break was perfect.