The England international grabbed a point for Roberto Martinez's side from the spot in a match which also saw Gareth Barry stretchered off after a foul by Jordi Gomez
The Black Cats were incensed at the decision to award the spot-kick, given after Seamus Coleman was brought down by Connor Wickham, although in truth Sunderland were fortunate the striker escaped a red card.
The equaliser set up a frantic finale with Wes Brown almost grabbing a dramatic winner only to see his goal-bound header cleared off the line by James McCarthy in stoppage time.Liam Bridcutt came in for suspended midfielder Lee Cattermole as Sunderland made four changes to the team that won 3-1 at Crystal Palace on Monday night.
An Everton side fresh from a 3-0 Europa League win over Lille was bolstered by Coleman, Samuel Eto'o and Ross Barkley.
The visitors quickly settled into a pleasing passing rhythm and Eto'o linked smoothly with fellow forward Romelu Lukaku to blast wide.
Wickham won a fifth-minute corner and the Sunderland forward's header from Larsson's resulting delivery brushed the roof of the net.
Everton midfielder Barry suffered an early end to his afternoon on a stretcher when Gomez caught his right ankle with a late tackle, aggravating a complaint the former England player carried into the match.
Sunderland were growing in confidence by the time Sylvain Distin hacked a Gomez cross out of the goalmouth, while Aiden McGeady offered Everton's response by sending a rasping drive narrowly over the top corner.
Barkley and McGeady exchanged passes to force a fine block from Bridcutt in the 35th minute before an error from Barry's replacement Darron Gibson saw Gomez force a fine save from Tim Howard.
Bridcutt largely impressed during the opening exchanges of the second half but the former Brighton player under hit an ill-advised backpass, his blushes spared as Costel Pantilimon rushed from his goal to deny Lukaku.
Referee Lee Mason entertained the Stadium of Light masses when he fell over due to a collision with McCarthy, shortly before Baines forced a far more significant tumble from Sunderland substitute Will Buckley - on for the ineffective Adam Johnson.
Larsson stepped up to curl a trademark effort beyond Howard, aided by a disorganised Everton wall, but Sunderland's lead proved short-lived.
Wickham lunged in to bring down Coleman, who dashed into the area on the end of a wonderful Eto'o pass, and Baines crashed home from the spot following prolonged complaints from the Sunderland players.
Sunderland edge three points clear of the relegation zone, although they might have been better off as Brown saw an injury-time header cleared off the line by McCarthy.