But United's push for a top-four place in the Premier League still suffered a huge setback with a rare and deft Phil Jagielka goal giving Everton a first-half lead and ensuring them a share of the points.
Jose Mourinho's side, whose form has been so underwhelming recently at their "Theater of Dreams", were facing the end of their 19-match unbeaten streak in the league as luck had earlier deserted them.
England center back Jagielka showed all the predatory instincts of a goal poacher, latching on to a Williams header from a 22nd-minute corner and, with back to goal, holding off Marcos Rojo to conjure up a shot that trickled between the legs of David de Gea.
His first goal of the season prompted an urgent response from United, with an Ander Herrera effort striking the bar, but even with Ibrahimovic back in the team, United were blunt.
There was misfortune, too, when Paul Pogba headed against the bar after the break before Ibrahimovic also had a headed goal ruled out for offside, with TV replays suggesting it had been the closest of calls.
(Reporting by Ian Chadband,; Editing by Neville Dalton)