The match had started quietly in terms of chances, but with both sides keen to assert themselves, there was an early battle in midfield.
Within the first 20 minutes, Hearts' Jamie Hammill and Flood of Aberdeen had gone into the book.
Although the home side had been on top during the early stages, they had goalkeeper Jamie Langfield to thank for keeping the scores level after he got down low to his left to block Ryan Stevenson's 12-yard shot.
And the Dons were dealt a blow midway through the half, as the influential Flood was forced off through injury. The former Dundee United man has only recently returned from a hamstring injury, and it looked as though he may have suffered a recurrence.
His replacement, Robson, was soon involved though, and had a hand in the opening goal after 25 minutes.
Robson's corner from the left caused mayhem in the box and Michael Hector just failed to connect as he attempted a shot. McGinn showed how alert he was to race in and blast home from 10 yards.
It was the striker's third goal in two games, and a fine strike which left Hearts keeper Jamie MacDonald helpless.
Robson became the third man to go into the book three minutes later, having broken from the defensive wall too quickly as Hammill's free-kick was blocked.
A neat reverse pass saw Robson slip in the impressive Peter Pawlett, who was unlucky to see his angled shot flash across the face of goal after 34 minutes.
The Dons had a big shout for a penalty two minutes later, following Hector's long throw.
Pawlett's shot was blocked on the line by Jordan McGhee, but referee Iain Brines was satisfied it had come off the defender's face rather than arm.
Seconds later, though, there was no denying McGhee handled McGinn's cross, and Brines pointed to the spot.
Usually reliable from 12 yards, McGinn aimed low to the right, but was denied by a fine save from MacDonald.
And the match hinged on a further setback for the Dons, the sending off of Robson just eight minutes after the restart. He picked up a second booking for bringing down Jason Holt in the midfield.
Hearts defender Dylan McGowan was shown the yellow card for a foul on Pawlett, before the Dons replaced Calvin Zola with Scott Vernon.
Hearts quickly responded with a double change, Holt and Scott Robinson replaced by David Smith and Callum Tapping.
Smith's impact was almost immediate as he struck a stunning volley which Langfield tipped onto the bar, only for a goal kick to be signalled by the referee.
Undeterred, Walker flashed a shot wide before he levelled matters. He neatly controlled a long free-kick as an uncharacteristically bewildered Aberdeen defence looked on, and rounded Langfield before slotting home.
Vernon thought he had put the Dons back in front as he got his head to a Johnny Hayes cross after 73 minutes, but 60 seconds later the turnaround was complete.
Walker found himself hitting the byline and sent across a perfect cut-back for Calum Paterson to run onto and fire home from eight yards.
With the game in its dying stages, Cammy Smith replaced Hector for the Dons as manager Derek McInnes went for broke, but it was a gamble that failed to pay off, as Hearts made it 3-1 in injury time.
Langfield went up for a Dons corner but Hearts won the ball and hit on the counter, Stevenson rounding the move off by drilling across the barely-repositioned keeper and into the top corner.