Everton looked to be on course to leave The Den with a win after Cenk Tosun put it ahead for the second time in the contest, but Jake Cooper's controversial equaliser — the defender diverted the ball into the net with his arm — gave Millwall hope and Wallace clinched the unlikely win deep into stoppage-time.
An otherwise tepid first half finally came to life just before the break, as Richarlison opened the scoring with a deflected long-range effort that squirmed under goalkeeper John Archer.
But Millwall levelled a few moments later, Lee Gregory beating Jordan Pickford with a fine looping header after Cooper flicked a set piece on.
With the scores still level just after the hour, under-pressure Everton boss Marco Silva introduced Tosun from the bench.
The Turkey international had a swift impact, linking well with Gylfi Sigurdsson and finishing into the bottom-right corner.
But Millwall equalised again three minutes later as Wallace's shot came back off Pickford and Cooper converted, infuriating Silva, who could see the incident on the stadium's big screen.
Wallace then got the winner deep into stoppage-time, tapping in from close range after another Millwall set-piece caused havoc in a ramshackle Everton defence.