Oussama Assaidi struck early in the second half before the left back salvaged a result from the spot, though Roberto Martinez's side still dropped out of the top four.
Oussama Assaidi netted four minutes into the second half after Kevin Mirallas had struck the woodwork twice for Roberto Martinez's men in the opening period.
With the match seemingly heading for a Stoke victory, Jermaine Pennant's reckless lunge on Leon Osman in the box handed Everton a spot kick at the death, which Baines duly dispatched.
Stoke welcomed Marc Wilson and Glenn Whelan back from suspension, while Everton made five alterations to the side which beat Southampton 2-1 on Sunday, including handing a first Premier League start to defender John Stones, who partnered Antolin Alcaraz in the heart of defense, with Phil Jagielka and Sylvain Distin both injured.
|VIEW FROM THE BRITANNIA
|By Alan Bond
Leighton Baines' late penalty earned Everton a hard-fought point against a determined Stoke City side.
Oussam Assaidi was impressive all afternoon and the on-loan winger struck cleanly past Tim Howard to open the scoring.
The first half was fairly even and Everton will feel desperately unlucky that neither of Kevin Mirallas' two excellent strikes found the net, the Belgian hitting first the bar and then the post in a lively early display.
Some great defending by Stoke in the second half looked like it would be enough to secure a third successive home victory. Blocks from Marc Wilson and Ryan Shawcross from Steven Naismith and Mirallas efforts were the closest that the visitors came but, in stoppage time, the pressure paid off and Everton took a share of the spoils in a fair result.
With rain teeming down at the Britannia Stadium, Mirallas had the best chance of the opening period as the match reached the half-hour mark, rifling a shot against the underside of the crossbar from 20 yards with Sorensen well beaten.
Ross Barkley then guided the ball just over from a Mirallas cut-back six minutes later, before the Belgian attacker struck the frame of the goal for a second time from a free kick as the sides went in at halftime all square.
Stoke, which is already without the injured Asmir Begovic, suffered a further goalkeeping blow at halftime, with Thomas Sorensen failing to re-emerge for the second half due to a reported Achilles problem. Jack Butland came on in his place to make his Premier League bow.
But those worries were soon forgotten when Assaidi – on loan from Everton's Merseyside rival, Liverpool - drilled home from the edge of the penalty area following a failed headed clearance by Stones.
Charlie Adam turned well on the edge of the penalty area to fire a left-footed effort straight at Tim Howard seven minutes later as Stoke assumed control of the fixture but Everton started to look dangerous again, with Barkley and Mirallas both having efforts blocked in the penalty area.
It looked as though the Potters were going to do just about enough to seal the three points but Pennant hacked down Osman in the penalty area in stoppage time to give the visitors hope. Baines coolly slotted home from the spot to rescue a deserved point for Everton, which dropped into fifth behind Liverpool as the Reds beat Hull City.