The Swede's 94th-minute penalty was awarded after Luke Shaw's goal-bound shot was handled on the line by visiting defender Ashley Williams, who was given a red card.
The point means United extend their unbeaten run to 20 games, but have now drawn nine times at home in the league and 12 overall, while opponents Everton missed the chance to leapfrog them in the table.
Everton's opener came through Phil Jagielka's clever, flicked finish from close range when he had his back to goal.
In response to going behind, Ander Herrera struck the crossbar after Joel Robles parried Daley Blind's free-kick and the United midfielder also forced Toffees goalkeeper Robles into a full-stretch save.
Paul Pogba came on for the second half and headed against the bar from Ashley Young's free-kick, while Ibrahimovic had a goal disallowed for offside in a disjointed United performance.