Marius Zaliukas, who was sent off the last time he played at Pittodrie back in December, added another red card to his growing collection for an off-the-ball kick at Chris Maguire after 64 minutes.
Jamie Smith should have given the Dons all three points but the Dons midfielder smashed the ball off the post with the goal gaping after Marian Kello had parried a Maguire effort.
The draw means Hearts remain five points ahead of the Dons in the race to secure one of the two lucrative Europa League qualification spots.
Jamie Smith returned to the Aberdeen starting 11 in place of Stuart Duff, while Javan Vidal came in for the suspended Mark Kerr.
Andrew Driver missed out through injury for Hearts who also made two changes. Laryea Kingston and Adrian Mrowiec were given starting berths with Greek defender Christos Karipidis suspended.
With Kerr absent, Richard Foster was given the task of man-marking Hearts' Portuguese playmaker Bruno Aguiar.
Calum Elliot's weak effort after four minutes, which rolled harmlessly wide for a goal-kick, was early evidence of why Hearts had failed to score in their last three.
With so much at stake for both teams it was a nervy start to the match with goalmouth action at a premium.
But the Dons could have opened the scoring after 16 minutes when Marian Kello flapped at a Charlie Mulgrew corner with the ball falling kindly into the path of Scott Severin at the back post but the former Hearts man shot into the side-netting.
The Slovakian keeper was called into action again after 23 minutes to thwart Smith's left-footed drive with a fine save.
Lithuanian defender Zaliukas then gave himself a tightrope to walk after earning an early caution for a trip on Gary McDonald.
Aberdeen's top scorer Lee Miller headed over the bar after 33 minutes following another accurate delivery from Mulgrew.
At the other end, Elliot fizzed a shot just wide of Jamie Langfield's left-hand post in a rare foray forward from the Jambos.
Hearts were forced to make a change five minutes before the break with the injured Kingston making way for David Templeton.
And the substitute almost made an immediate impact when he skipped past four Aberdeen players before his eventual effort was pushed round the post by Langfield.
The visitors made a bright start to the second half with Zaliukas firing a free-kick harmlessly over the bar from all of 40 yards two minutes after the restart.
The Aberdeen supporters were then left wondering how their side hadn't taken the lead after 53 minutes when Kello could only parry Maguire's shot into the path of Smith but the Dons midfielder somehow smashed the ball off the post with the goal gaping.
A well-struck shot by Sone Aluko then stung the palms of the Hearts goalkeeper as the Aberdeen pressure intensified.
Hearts were then reduced to 10 men after 64 minutes when Zaliukas was shown a straight red card for an off-the-ball kick at Maguire.
The Dons should have capitalised on their numerical advantage after 79 minutes but Smith dragged his effort wide of the target from a good position.
Stuart Duff then replaced the Aberdeen midfielder who limped off with an injury after 81 minutes as the match came to a thrilling climax.
The home side threw everything at Hearts in the closing stages with Foster going close in the final minutes.
However Csaba Laszlo's side managed to hang on for a precious point, although Christian Nade could have won it at the death but shot wide.