Marcus Rashford inspired England to the victory required to top Group B and ensure it was despair for Wales as they went out of the tournament after a bitterly disappointing World Cup campaign.
Wales needed to either beat England and hope Iran and USA ended in a draw or pursue the more unlikely outcome of running up a four-goal victory margin at Ahmad bin Ali Stadium.
England, who now face Senegal in the last 16 on Sunday (19:00 GMT), ensured neither scenario was ever a serious consideration as they dominated throughout and took full control after an uneventful first 45 minutes.
Wales manager Rob Page was forced to replace Gareth Bale at half-time because of an injury, although the great talisman had only had seven touches in an anonymous display.
And any hope of Wales qualifying for the last 16 was wiped out as England scored twice within six minutes of the restart.
Rashford fired a free-kick past Danny Ward following Ethan Ampadu’s foul on Phil Foden after 50 minutes, with the Manchester City midfielder then marking his return to England’s team moments later by turning in Harry Kane’s cross at the far post.
Wales were demoralised and outclassed as they knew they were on the way home from Qatar and Rashford added his second in the 68th minute, with a large slice of help from Wales keeper Ward, in for suspended Wayne Hennessey after his red card against Iran, who allowed a fierce shot to slip through his legs.
England top Group B with seven points, two points ahead of the United States who set up a last-16 meeting with the Netherlands by beating Iran 1-0 in their grudge match, while Wales finished bottom of the table with a point.
England and Southgate have achieved their first priority of qualifying for the last 16 while topping their group, two strong wins against Iran and Wales coming either side of that dismal USA showing.
It represents a job satisfactorily done by England – now they must take the next step against the dangerous African champions, Senegal.