The visiting Dons opened the scoring in the 14th minute when Mackie took advantage of an error by defender Marius Zaliukas.
However, left-back Wallace equalised just seven minutes later, working a one-two with Christian Nade before finding the net.
Hearts were denied a penalty at the end after Steve Conroy changed his mind on pointing to the spot for Jamie Langfield's challenge on Michael Stewart after conferring with the assistant referee.
It was clear from the start of the Scottish Premier League match that the blustery conditions were going to have an adverse affect on proceedings.
Aberdeen seemed to adapt well and registered the first attempt on goal after four minutes.
Zander Diamond rose high to meet Sone Aluko's corner but he was unable to keep his header down as it cleared the crossbar.
Aberdeen then took the lead after a glaring mistake by defender Marius Zaliukas in the 14th minute. The Lithuanian allowed Andrew Considine's pass to run past him and Mackie raced in to slip the ball under Janos Balogh from a tight ankle.
That lead lasted a mere seven minutes, however, as Wallace created and finished the move. The left-back cut in from the flank and played a one-two with Christian Nade before sliding in to lift the ball over Langfield and high into the net.
The hosts were keen to capitalise on the momentum built up from levelling the score as they put the Dons defence under pressure in search of another.
The central midfield trio of Christos Karipidis, Michael Stewart and Bruno Aguiar made their numerical advantage count in that position as they began to dominate.
Both teams were not helped by the build-up of water on the pitch as a consequence of the driving rain, with passes getting held up.
Aguiar's dangerous delivery from corner kicks was causing the visitors problems and Aberdeen were relieved to see Saulius Mikoliunas head the ball wide in the 34th minute.
Hearts returned for the second half in determined mood and continued to keep the Dons on the back foot.
Nade, without a goal in nine months, should have done better in the 54th minute from Aguiar's corner but he somehow headed over from under the bar.
Hearts goalkeeper Balogh was thankful he only conceded a corner and not a goal in the 56th minute when he let Scott Severin's cross slip through his hands.
And the Hungarian breathed a sigh of relief from the subsequent set-piece when Jared Hodgkiss picked up a loose ball and unleashed a powerful strike from 18 yards which rattled the bar.
At the other end, moments later, Langfield made a diving save to deny Christophe Berra from Stewart's free-kick.
As the match entered the final quarter, either team was more than capable of hitting the winner.
Considine was afforded time at the corner of the box for Aberdeen and his left-footed strike caused problems as it deflected goalwards but Zaliukas cleared the danger.
In an absorbing contest, the match swung from one end to the other.
Aguiar bulleted a header wide in the 74th minute after connecting at the back post with Nade's cross before Lee Miller's long-range shot struck the outside of the post seconds later.
Controversy gripped Tynecastle in the 85th minute when referee Conroy initially gave Hearts a penalty following Langfield's challenge on Stewart but changed his mind after talking with assistant Chris Young.
The woodwork then saved Aberdeen in injury-time when substitute Deividas Cesnauskis darted into the box before hitting a shot off the post.
The rebound fell to Jamie Mole but he blasted over from close range.