The left-back converted from the spot 14 minutes before full-time to cancel out Sebastian Larsson’s free-kick as the Blues were forced to settle for a 1-1 draw on Wearside.
Everton, however, face an anxious wait to determine the severity of an injury to Gareth Barry who was stretched off in the first half with a leg injury.
The draw means Everton extend their unbeaten run to six matches and remain 10th in the table heading into the third international break of the season.
Samuel Eto’o was back in the team after not featuring against Lille – and the Cameroon striker almost capped what would have been a superb team goal not long into the contest.
The striker, playing just off Romelu Lukaku, exchanged a succession of passes with the Belgian in the Sunderland half but his finish from 12 yards – uncharacteristically – lacked composure.
It was a lively start, with Conor Wickham heading onto the roof of the net from a Sebastian Larsson corner in the hosts’ first attack.
Then came the worrying sight for Evertonians when Gareth Barry was stretchered from the field with his right leg in a brace just a quarter of an hour into the game.
The midfielder, who was also forced off against Lille in midweek but deemed fit to start at the Stadium of Light, was caught late by Jordi Gomez and after received several minutes of treatment before he was carried from the field.
Darron Gibson was Barry’s replacement and he fired over from long-range not long after his introduction, while Lukaku was also off-target with an effort from a similar position.
Everton persisted on trying their luck from distance – and they got closer each time. McGeady was inches away with an angled 25-yard effort which had Costel Pantilimon beaten but flashed agonisingly past the post.
Ross Barkley, after combining excellently with Seamus Coleman, then saw a goal-bound shot blocked by Liam Bridcutt as Everton pushed Sunderland further back without finding a cutting edge in front of goal.
There were fleeting moments of danger for the Everton rearguard, with full-back Anthony Reveillere an outlet on the left for the Black Cats. On one particular occasion, the Frenchman delivered an excellent low centre but Sylvain Distin was perfectly-placed to make a last-ditch clearance.
Gomez was lucky to find himself still on the pitch late in the first half when he appeared to dive on the edge of the Everton box. He had earlier been booked for the challenge which had led to Barry’s injury, but referee Lee Mason chose not to give the midfielder a second yellow card for simulation, much to the annoyance of the travelling Toffees.
Everton would have felt doubly aggrieved had Gomez then scored with a drive from the edge of the box shortly before the interval, but fortunately Tim Howard was alert to make his only save of note in the first half.
The Blues raced out of the traps after the restart but could not make a period of concerted pressure count.
Pantilimon saved well from Barkley before racing from his line to dive at the feet of Lukaku who had broken free and tried to round the Sunderland goalkeeper instead of shooting.
Lukaku was again thwarted by the Sunderland goalkeeper moments later, this time crashing in a left-foot shot which was palmed onto the outside of the post. And once more, the Belgian was denied by Pantilimon who clutched a header destined for the top corner.
The Blues were made to pay for not converting one of these openings and, in typical sucker-punch fashion, Sunderland took a 67th-minute lead courtesy of Larsson's precise free-kick.
Baines tripped substitute Will Buckley five yards outside the area and from the resulting set-piece, the Sweden international bent the ball up and over the wall, past Howard’s dive and into the net.
The Blues were only behind for nine minutes, however, as Baines atoned for conceding the free-kick by levelling from the spot.
Coleman, latching onto a defence-splitting pass from Eto’o, was chopped down by Conor Wickham inside the area. Sunderland’s players protested but it was a clear foul, and Baines tucked the ball under Pantilimon to make it 1-1.
There was still time for one team to win it – and Sunderland very nearly did late on, only for James McCarthy to make what proved to be a point-earning goalline clearance deep into stoppage time.