Hearts winger Andrew Driver had the first chance of the match in the eighth minute and, with no options in the middle, he chose to shoot from a tight angle but it was saved well by Yves Makaba-Makalamby.
Down the other end minutes later, the ball broke to Chris Hogg in the box but Christophe Berra did well to hassle the Hibs skipper and the ball flew over.
With play going from end-to-end, Hearts came very close to taking the lead on 16 minutes.
Robbie Neilson tossed a long throw into the box, Christian Nade flicked the ball on well only to see his header loop onto the crossbar with Makaba-Makalamby beaten.
The visitors had their best opportunity of the half midway through. Lewis Stevenson set up Steven Fletcher 18 yards out but, even on his favoured left foot, the striker blasted high and wide.
With the Hearts midfield starting to get on top, the home side forced a couple of saves from Makaba-Makalamby around the half hour.
First Laryea Kingston and then substitute Gary Glen forced the big keeper into action.
Just before the break came as fine a piece of defending as you are likely to see this season.
Derek Riordan looked to have time to pick his spot after a quick break but from nowhere Eggert Jonsson hooked the ball away from the striker's feet with a fine tackle.
Jonsson was in the thick of it again five minutes into the second half.
The Icelandic international got free down the left and picked out Nade well but his first-time shot came back off the post and was cleared to safety.
Hearts were dominating the second half and youngster Glen was so unlucky not to put them ahead in the 55th minute.
The ball broke to him in space 25 yards out and he fizzed an effort at goal, only to see it clip the top of the crossbar.
The home side had a number of chances which never tested the Hibs keeper.
Nade was particularly guilty as he blazed over from close range with just 15 minutes left.
Hearts were nearly left to rue their profligacy in front of goal as Fletcher bustled his way past a couple of weak challenges but his shot was blocked low down by Janos Balogh.
It would have been harsh on the hosts, who deserved the points from this one.