Lee Miller put the home side in front three minutes before the interval, heading home Michael Paton's cross from close range.
But Hearts levelled through prospective Scotland cap Andrew Driver after 63 minutes, the Oldham-born winger coolly slotting home substitute Christian Nade's pass.
Aberdeen lined up with 16-year-old Fraser Fyvie in midfield in the only change to the side that had started in the draw with Kilmarnock a fortnight ago. Chris Maguire dropped to the bench.
The hosts remained without the services of long-term injury victim Zander Diamond and Davide Grassi, as wl as centre-back Jerel Ifil who has been struggling with 'flu after a hamstring complaint.
Sone Aluko found a place on the Dons bench after his exploits with Nigeria at the Under-20 World Cup.
The visitors remained unchanged despite their defeat to St Mirren before the international break.
Csaba Laszlo's side were again without highly-rated striker David Templeton and Lithuanian defender Marius Zaliukas through injury.
Hearts began the afternoon three points behind their hosts, and were looking to bounce back after becoming the first side to lose on league duty at the new St Mirren Park.
The visitors started brightly and were unlucky, after Craig Thomson's half-cleared corner was sent back in, not to go ahead. Jose Goncalves brought the ball down, but his left-foot strike was deflected wide of the upright.
Aberdeen threatened just after the quarter-hour when Andrew Considine headed over a Charlie Mulgrew free-kick from six yards.
And after 24 minutes another Thomson corner, this time form the right, saw Suso Santana flash a header across the face of goal from eight yards.
Aberdeen were soon on the attack, but after Peter Pawlett's challenge had seen the ball break loose to Paton on the edge of the area, the former Brechin City loanee saw his shot comfortably gathered.
The home fans were incensed on 29 minutes when Pawlett's drive into the area was brought to an end by the strong challenge of Ismael Bouzid, but in reality there was no danger of a spot-kick being awarded.
However, the hosts took the lead after 42 minutes. Pawlett and Mulgrew combined on the left to release Paton, and although there was a touch on his cross, the ball found its way to Miller who nodded home at the back post.
Aberdeen, after taking the lead so late in the first half, had come out looking the more confident side.
Fyvie in particular impressed, and it was his pass that set up Gary McDonald for a 18-yard shot which was charged down.
A minute later, the teenager's wickedly inswinging delivery from a left wing corner left Hearts goalkeeper Janos Balogh pleased to have pushed over the crossbar.
Another Fyvie delivery saw Pawlett presented with a chance after Balogh had failed to punch convincingly clear, but the young midfielder sliced his 15-yard effort high and wide.
Pawlett was to be replaced by Aluko soon after, the midfielder forced off by a hamstring injury.
Hearts had brought on Nade for the largely ineffectual Witteveen, and the former Sheffield United man was involved in their equaliser after 63 minutes.
He slipped in Driver, who picked his spot from 15 yards with a curling effort beyond Jamie Langfield.
Miller found another good angle after 74 minutes, but his effort was beaten away by Balogh at his near post. Mulgrew's resultant corner was cleared as far as Fyvie, but Obua was well placed to clear off the line.
With four minutes remaining, a Thomson corner found Ruben Palazuelos free in the middle of the penalty area, but Langfield was able to push his header over the crossbar.
Hearts could have won it right at the death as Langfield failed to clear a corner, but a mass of bodies in front of the home goal prevented Goncalves, Obua and Nade from finding the target.