Hearts claimed a record sixth clean sheet in a row at Pittodrie to end 2017 with a nine-match unbeaten run.
It is the first time in the Edinburgh club's 143-year history that they have gone six matches without conceding, although they had striker Kyle Lafferty red carded two minutes from the end.
Aberdeen's second-half onslaught looked like it might result in a winning goal but the Hearts defence remained firm and dogged. They now enter the New Year undefeated since the start of November.
Lafferty's red card was for a lunging tackle on Grame Shinnie, which enraged the home players and supporters. He was shown an instant red card and was cheered as he left the field. The Aberdeen fans still hold a grudge against the Northern Irishman from his altercation with Charlie Mulgrew at Ibrox as a Rangers player.
Hearts arrived at Pittodrie with a catalogue of injuries and would lose two more players during the course of a competitive 90 minutes. Key men including Arnaud Djoum, Jamie Walker, Prince Buaben and Connor Randall were all missing to begin with.
That resulted in six teenagers in the visitors' matchdays squad - Anthony McDonald, Harry Cochrane and Jamie Brandon in the starting line-up, with Daniel Baur, Alex Petkov and Euan Henderson amongst the substitutes.
Aberdeen replaced Greg Stewart with Kari Arnason from their midweek win over Partick Thistle as manager Derek McInnes kept a settled team. They had the game's first effort on target, an overhead attempt from striker Adam Rooney which didn't overly trouble the Hearts goalkeeper Jon McLaughlin.
The next task for McLaughlin was to gather Kenny McLean's dipping cross. Hearts' injury problems worsened on 17 minutes when Michael Smith was forced off and replaced by 18-year-old Baur, who was making only his second senior appearance. He lined up at left wing-back despite being a centre-back to trade. Brandon switched to Smith's position on the right.
Aberdeen were in the ascendancy but Hearts ought to have taken the lead on the half-hour mark. Esmael Goncalves sent David Milinkovic clean through on goal, however the Frenchman could only watch in dismay as Joe Lewis emerged to block his effort near the penalty spot.
The visitors were then forced into another change when McDonald trudged off clutching his thigh. Lafferty took his place, although the flow of play towards McLaughlin's goal continued. The Englishman was at his best on 42 minutes to deny Rooney certain opener after Andy Considine's shot deflected into the striker's path. McLaughlin's instinctive save ensured this affair remained goalless at the interval.
Hearts' resilience was also partly attributable to their three central defenders, John Souttar, Aaron Hughes and Christophe Berra. They headed, tackled, blocked and cleared as ball after ball arrived in the penalty area.
McInnes brought Stewart off the bench for the second half and an opportunity fell to him on 58 minutes. Berra's headed clearance landed with the forward, who chested the ball and volleyed it at goal only to see it deflected for a corner. The resultant delivery saw another sublime save by McLaughlin from Scott McKenna's netbound header.
When McKenna's diving header from Stewart's free-kick landed wide, the notion began to arrive that Aberdeen's relentless pressing may come to nothing. Each time they carved a path through the tight Hearts rearguard, they were met with a block, a sliding challenge or a save.
The Tynecastle side were playing on the break and were disappointed not to make more of low crosses into the Aberdeen penalty area from Brandon, Milinkovic and Don Cowie. Then came a glorious chance for Goncalves with ten minutes left. Played in by Milinkovic on the left, the Portuguese could only lament a bobble on the pitch which caused him to shoot high into the crowd.
Hearts' primary concern in the closing stages minutes was to preserve that clean sheet. The Aberdeen fans appealed loudly for handball against Brandon inside the penalty box but referee John Beaton was unmoved.
Then came Lafferty's dismissal for serious foul play. He lunged in late from behind on Shinnie and was shown a straight red card by Beaton with just two minutes remaining. His team-mates battled on to earn a point and inscribe their names into the Tynecastle record books.
Aberdeen (4-2-3-1): Lewis; Logan, Arnason (Maynard 81), McKenna, Considine (Stewart 46); O'Connor, Shinnie; Christie, McLean, Mackay-Steven (Wright 81); Rooney.
Unused subs: Rogers, Reynolds, Harvie, Ball.
Hearts (5-4-1): McLaughlin; M Smith (Baur 17), Souttar, Hughes, Berra, Brandon; Milinkovic, Cowie, Cochrane, McDonald (Lafferty 35); Goncalves.
Unused subs: Hamilton, Martin, Stockton, Petkov, Henderson.
Referee: John Beaton.