The full-back blasted past keeper Keiren Westwood from 12 yards after referee Howard Webb had ruled that Leon Osman had been fouled inside the box, although claims from the home players that he had simply kicked the ground appeared to be borne out by television replays.
Baines' effort cancelled out Jack Colback's first senior goal for the Black Cats, a deflected 26th-minute shot against the run of play which galvanised his side as they attempted to win for the third time in manager Martin O'Neill's four games to date.
Baines' equaliser also extended Sunderland's wait for a victory over the Toffees to 15 games with the visitors unbeaten at the Stadium of Light for a decade.
The game, which was broadcast by the BBC World Service to an estimated audience of 25 million across Africa, very nearly came to a dramatic conclusion when Sylvain Distin turned Stephane Sessegnon's cross into the side-netting.
However, the big talking points as a crowd of 43,619 headed home were the decision which handed Baines his big chance, and Sunderland's paltry return of just four wins on their own pitch in 2011.
So often this season, the Black Cats have dominated the opening stages of games and failed to take advantage of the chances they have created, a failing which ultimately cost Steve Bruce his job.
Today, the story was markedly different as they endured a torrid opening 20 minutes or so.
Everton, themselves on an upward curve after their midweek victory over Swansea, dominated the early exchanges and created at least three gilt-edged opportunities to take the lead.
Tim Cahill, who has not scored for his club since December 20 last year, might have ended his drought with just seven minutes gone when full-back Tony Hibbert's long ball played him in on the right side of the penalty area.
The Australia international struck his shot from a tight angle well, but Westwood beat the ball away.
Cahill should have done much better seven minutes later when he was presented with a free header from Baines' corner, but powered his effort well wide.
Striker Louis Saha was equally wasteful in similar circumstances two minutes later, this time with Royston Drenthe the supplier, as the defensive resilience which has returned under O'Neill deserted Sunderland.
Their cause was not aided with 21 minutes gone by Titus Bramble's premature exit to injury, which saw Phil Bardsley switch from left-back to right-back, John O'Shea push inside with Wes Brown and Kieran Richardson drop in on the left with Colback replacing him in midfield.
But it was Sunderland who took the lead five minutes later and it was the newcomer who did the damage.
Sessegnon skipped past Distin and Hibbert before slipping the ball to the unmarked Colback, whose shot clipped the recovering Frenchman and flew past the helpless Tim Howard.
In an instant, the uncertainty and lack of cohesion which had characterised the Black Cats' performance during the early stages evaporated, and they started to take the game to Everton with Sessegnon and Bendtner repeatedly finding space.
However, Everton got themselves back into the game within six minutes of the restart, although they did so in controversial circumstances.
Osman was allowed to work his way into the penalty area, where he went down as Wes Brown and Lee Cattermole closed in on him.
Referee Webb took his time, but eventually pointed to the spot, although replays suggested that neither Sunderland man had touched the midfielder and that he had actually kicked the ground.
But as the home fans bayed, the nerveless Baines smashed his spot-kick high to Westwood's left to level.
Clearly aggrieved by the turn of events, the Black Cats set about the task of restoring their lead in determined fashion, and Hibbert had to clear away a Richardson corner from under his crossbar while Saha headed Sebastian Larsson's effort from the other side on to the roof of his own net.
However, Westwood was relieved to see Osman head across the face of goal after meeting Drenthe's driven 63rd-minute cross.
Sunderland battered away in the search for a last-gasp winner, but the closest they came to getting it was when Distin deflected Sessegnon's 90th-minute cross into the side-netting.