The draw keeps Villa in fifth place, just one point ahead of Everton, who gave themselves a welcome boost ahead of next Sunday's FA Cup semi-final against Manchester United.
In a pulsating encounter, only a courageous fightback on the part of Villa enabled them to restore some recent lost pride.
They were two goals down in the first half through Marouane Fellaini and Tim Cahill and Villa fans feared the worst as their favourites were seemingly heading for their fifth successive defeat.
But big John Carew put them back on course only for the hugely talented South African Steven Pienaar to give Everton a 3-1 lead.
James Milner scored direct from a free-kick and then Barry slammed home the face-saving penalty to rob Everton of their first away win since Boxing Day when they won at Middlesbrough.
The game certainly lived up to its high-scoring reputation with Villa fully aware that it was Everton who began their problems way back in February in the FA Cup when they gained revenge for the 3-2 home defeat inflicted by the Birmingham club in December.
But Everton, winners of three of their previous four games and in smart goalscoring form with ten goals in this period, were also up for the fight and in the space two minutes seemingly destroyed Villa.
With tiny Leon Osman showing some fine skill Everton opened up the Villa in alarming fashion, but the destruction of the home side still came as a big surprise.
Skipper Philip Neville, making his 400th league appearance, began Everton's sudden surge.
He picked up a half-hearted Zat Knight clearance and hammered in a rising drive which Brad Friedel tipped over the bar.
This incident appeared to inject Villa's defence with a dose of unadulterated panic.
Jo was always a slippery customer and he set up Leighton Baines to produce a left-wing cross which Fellaini forced home from close range in the 20th minute.
The goal was a massive shock to Villa's system and Pienaar went just wide with a rasping shot.
But there was no respite for Villa as in the 22nd minute, Cahill popped up for ninth goal of the season.
Pienaar provided a the cross from the left which Cahill headed against the bar and then headed in the rebound.
Despite the shock of going two goals behind, Villa attempted to repair the damage and pulled back a goal in the 33rd minute when Carew notched his 13th goal of the campaign.
Milner's right-wing cross was knocked back by Barry to Gabby Agbonlahor and the ball went into the path of Carew to lash his close-range shot past Tim Howard.
Any hopes of a Villa revival were seemingly dented in the 53rd minute when Pienaar collected a short pass from Neville, hoodwinked Luke Young and left Friedel flat-footed with an accurate 20-yard shot.
Villa, however, stormed back into contention when Milner lashed a 25-yard free-kick past Howard for his sixth goal of the season after Joleon Lescott had brought down Carew.
Lescott was in further trouble in the 65th minute when he attempted a high kick clearance only to impede Stiliyan Petrov to concede a penalty which Barry blasted into the roof of the net to set up a hectic finish.