At a rain-soaked St Mirren Park, Dons striker Lee Miller hit the post with a header in the first half and the visitors missed a couple of good chances early in the second period.
In the 77th minute, when Dons stopper Zander Diamond failed to cut out a Billy Mehmet cross, Craig Dargo struck from close range and it looked like that would give the Saints their first home win of 2009.
However, the Pittodrie men were not to be denied and in the third minute of added time, Wright, on for Miller just before the break, bulleted his header past Paisley keeper Chris Smith for a deserved leveller.
Victory was snatched from Gus MacPherson's side but it was still an improvement on Saturday's 7-0 mauling at Celtic.
That result had left the Paisley side - and keeper Smith in particular - searching for some confidence.
The St Mirren keeper, however, spectacularly misjudged Charlie Mulgrew's wonderful whipped-in free-kick in the eighth minute but went unpunished when Miller's header nicked the post before spinning wide, the disappointment of the travelling fans at the far end who thought the ball had gone in.
The Buddies raced up the park and David Barron's cross from the right, equally accurate, was met by midfielder Andy Dorman but he flicked the ball wide of the far post.
The incessant rain was influencing the game with the ball speeding around the pitch although at times with no great purpose.
The home side's best chance of the half came when they broke quickly in the 16th minute through Dargo.
The former Kilmarnock striker sent Dorman in to the box with a perfectly-weighted pass but Dons keeper Jamie Langfield bravely blocked the attempted chip from 10 yards and the danger was cleared.
In the 31st minute Smith made up for his earlier mistake when he produced a good save from Lee Mair's half-volley after the former Dundee player latched on to a Miller knock-down 20 yards from goal.
Then, the back-tracking Dons skipper Scott Severin took the ball from Garry Brady's toes at the edge of the Aberdeen box as the St Mirren midfielder, set up by the energetic Dargo, set himself to shoot.
The visitors were dealt a blow in the 40th minute when Miller limped off to be replaced by Wright who should have scored within a minute of the restart.
Seconds into the second half Aberdeen wide-man Chris Maguire sent in an inviting cross from the right which evaded Smith but Wright failed to connect at the far post, the Dons substitute sliding into the goal as the ball skipped past.
The Dons looked more eager and in the 52nd minute, from a similar position, Maguire sent in another great cross but this time Darren Mackie scooped the ball over the bar from barely six yards out.
In the 58th minute Stuart Duff replaced Javan Vidal and moments later Smith injured himself sliding out to block Mackie who had raced through the centre of the Saints defence.
Smith recovered after treatment but as the game slipped past the our mark, the home side had yet to really test his opposite number since changing ends, a Dargo shot aside.
That should have changed in the 63rd minute but Brady missed the target by a foot after being set up by Dargo at the edge of the Aberdeen penalty area.
In the 77th minute the home side took the lead after a mistake by Dons defender Diamond.
When Mehmet drove a cross in from wide on the right, Diamond should have cleared but missed his kick allowing Dargo to knock the ball in from close range.
As rain turned to snow, Aberdeen tried to rally but it was Langfield who pulled off a great save from Barron with two minutes remaining.
In the final minute Mair headed a Mulgrew corner over the bar from eight yards out but in the third minute of injury-time, with all hope seemingly gone, Wright headed a dramatic equaliser from Sone Aluko's cross.