Everton struggled to create goal-scoring opportunities until Andre Gomes' cross found the diminutive, Walcott who headed home three minutes from time.
"The lads are devastated in the dressing room because we deserved more out of the game," Villa manager Dean Smith said.
"I thought in the last eight minutes we got a bit sloppy on the ball and didn't take as much pressure off ourselves as we needed to."
Smith was unimpressed by Villa's lack of composure in the closing stages, with forward Anwar El Ghazi smashing the ball over the crossbar from close range.
"It was one that probably should've gone into the back of the net, but it doesn't and unfortunately they went up the other end and score," Smith said.
"I think Theo's trying to head it back across goal which makes it even more disappointing."
The result left Villa 19th in the table, three points adrift of the safety zone, having played a game more than 17th-placed Watford.
Everton extended their winless run to four league matches to stay 11th in the table, having failed to mount a challenge for European qualification spots since the league resumed last month.