There were few clear-cut chances which came as no surprise - before the game only leaders Celtic had conceded less than the 19 goals both sides had let in in the Scottish Premiership season so far.
But Aberdeen emerged victorious thanks to Flood's late goal.
Aberdeen made two changes from their win over Kilmarnock. Loan signing Alan Tate was handed a debut after Michael Hector's temporary spell at the club had come to an end, while captain Russell Anderson dropped to the bench to be replaced by Joe Shaughnessy.
Terry Butcher's Hibs were unchanged from the side that had let a two-goal lead slip against Dundee United last weekend.
He went down, seemingly under the challenge of Langfield, but Hibs' penalty claims were waved away.
It was perhaps telling that Heffernan made no issue of the decision, but the home support were relieved nonetheless.
It was Butcher's men who made much of the running in the opening period, but without causing too much concern for goalkeeper Langfield.
It was midway through the first half before the Dons began to impress themselves on the game, forcing a series of corners before having a penalty claim of their own.
There was much more pressure on referee Craig Thomson this time, with the majority of the 12,734-strong crowd appealing for the spot kick after Michael Nelson clearly handled Peter Pawlett's cross from the right - but again the referee was unmoved.
That brought the crowd to life, and from a Barry Robson corner, Hibs keeper Ben Williams had to be alert to deny Reynolds a second goal in as many games.
The driving runs of Pawlett from an advanced midfield position have been a revelation for Aberdeen this term, and it was one such burst which brought about the first booking of the match, Scott Robertson cautioned for bundling the midfielder over.
Aberdeen finished the half the stronger of the sides, but could have shot themselves in the foot when Heffernan pounced on Jonny Hayes' slack pass, but fired wide of the upright.
Niall McGinn had flashed a low shot wide of Williams' left-hand upright, and on the stroke of half-time there was another, far less convincing claim for a spot-kick as Shaughnessy tumbled in the area.
Like the first half, the second was slow in getting started, although Hayes almost played himself into trouble. His attempted pass out of defence was cut out by Robertson, but Hayes recovered well.
Irish Under-21 international Shaughnessy became the second man booked for a crunching tackle on Lewis Stevenson 10 minutes after the restart.
Paul Cairney drew a save from Langfield with a free-kick from distance, before McGinn headed wide from a Robson cross at the other end.
Hibs were first to show their cards from the bench, with 19-year-old Sam Stanton replacing the experienced Robertson in midfield, before Jordan Forster's trip on Pawlett saw him become the third man booked.
The visitors' second change saw Heffernan departing the fray to be replaced by another youngster, Jason Cummings, who has been handed his chance in the senior squad since the arrival of Butcher.
Their final change, with 10 minutes left, was a straight swap on the right, Alex Harris replacing Cairney.
It was three minutes later before Aberdeen made their first change, and it was another straight swap, with Calvin Zola taking Scott Vernon's place up front.
The game looked to be petering out towards a 0-0 draw, before Flood stepped up to fire an unstoppable shot into the corner of the net from 20 yards with just four minutes left.
The Dons swapped Anderson for Hayes and Josh Magennis for McGinn as they played out the final few minutes to seal the points and secure their grip on second spot.