The Dons enjoyed the better of the chances against a Hearts side that looked jaded after their midweek exertions against Liverpool in the Europa League, although the Tynecastle men remain unbeaten in the SPL this season.
Despite their pressure, the hosts were unable to find a way past Hearts stopper Jamie MacDonald and were forced to settle for a second successive goalless draw at home.
Aberdeen made only one change to the team that defeated Morton 2-0 after extra time in the Scottish Communities League Cup midweek with captain Russell Anderson returning at the expense of the injured Stephen Hughes.
David Templeton was a notable absentee for the visitors because of suspension with Andrew Driver stepping in to replace him.
Apart from that enforced change, John McGlynn stuck with the same team that were defeated 1-0 by Liverpool on Thursday.
Dons had made a solid start to the season as they looked to end a barren run of seven SPL matches against Hearts without a goal.
The game began at a frantic pace with Arvydas Novikovas flashing a shot wide of the Aberdeen goal before the Lithuanian midfielder found John Sutton in space but the striker's effort was bravely blocked by Gary Naysmith.
The Dons had half-hearted appeals for a penalty waved away when Ryan Jack tumbled to the ground in the box following a clumsy challenge by Darren Barr.
Aberdeen ended the half strongly and should have opened the scoring after 37 minutes when Gavin Rae played a defence-splitting pass into the path of Jack but the midfielder was unable to dink the ball over the advancing MacDonald.
The Dons went painfully close to netting on the stroke of half-time when Jack burst down the line and cut the ball back for Scott Vernon whose effort cannoned back off the crossbar.
The visitors made a change at the break with Marius Zaliukas, who had been nursing a thigh injury, replaced by Denis Prychynenko.
The Dons made a bright start to the second half with MacDonald just managing to keep out a Jack volley and Vernon turned the rebound onto the post, although the striker was offside in any case.
Naysmith, playing against the club where he started his career, hobbled off with a hamstring strain just before the hour mark and was replaced by Chris Clark.
Aberdeen threw on Josh Magennis and Rory Fallon in the closing stages in the hope of finding a winner but it was Andrew Considine who could have been the hero had he managed to keep his header from a Jonny Hayes corner under the crossbar.
And it was Hearts who almost stole all three points when Driver hit the post with the last kick of the match.
Thomas Reilly's injury time leveller handed St Mirren a share of the points in a 1-1 draw against Motherwell at Fir Park.
The visitors were rewarded for spells of dominance by a last-gasp goal after Micheal Higdon took advantage of some poor defending by Lee Mair and slotted beyond Craig Samson in the opening minute.
St Mirren pressed for an equaliser throughout the remainder of the match and Shaun Hutchinson was dismissed in the closing stages.
It was the last minute of injury time when Steven Thompson forced an excellent save from Darren Randolph before substitute Reilly bundled the ball into the net.
Motherwell boss Stuart McCall handed first-team debuts to both Steven Hetherington and Fraser Kerr, following knocks to Chris Humphrey and Tom Hateley in Thursday evening's 2-0 Europa League defeat to Levante.
The home side got off to a dream start when Higdon capitalised on some hesitant defending by Mair before calmly slotting the ball beyond Samson in the opening minute. But the visitors responded in a positive fashion and only a brave block from Adam Cummins prevented Thompson profiting from Dougie Imrie's pin-point delivery.
Thompson passed up a good opportunity to level the game six minutes before the break - losing his footing as he prepared to have an effort on goal. Motherwell responded at the other end but Higdon could only produce a weak effort directly at Samson.
Throughout the second half St Mirren continued to press for a leveller and Lennon brought on Reilly for Parkin in an attempt to boost their attacking threat.
Hutchinson received a yellow card for dissent with 10 minutes remaining and with three minutes remaining he was sent off for the second time in as many matches when he lunged in on Reilly - much to the anger of the home support.
Four minutes of injury time presented the visitors with hope of grabbing an equaliser and after Randolph did brilliantly to deny Thompson, Reilly fired home to deny Motherwell the chance to move top of the league table.