Neither goalkeeper was particularly busy in a match which ebbed and flowed, but ultimately there was a lack of quality in front of goal.
Dundee United threatened first when Craig Conway cut inside Robbie Neilson but curled his shot just over the top.
Bruno Aguiar tried to respond after a flowing Hearts move but his effort was over-ambitious and it drifted well wide.
But United had the better of the opening exchanges and took a firm grip of the midfield, even if goalmouth incidents were few and far between.
Laryea Kingston looked the one player capable of sparking something for Hearts and he at least tested Lukasz Zaluska with a deflected shot midway through the first half.
Lee Wallace then cut the ball back for Andrew Driver but Lee Wilkie was alert to the situation and made a fine block.
Christian Nade was replaced by David Obua just seconds after a wild challenge on Paul Dixon which earned him a yellow card when it could have been red.
Two minutes from the break, Kingston sent an inviting ball across the six-yard box but none of his team-mates could take advantage.
Driver then tried his luck from a tight angle but the ball was deflected wide as Hearts finished the first half strongly.
Hearts had a chance early in the second half after some slack play by Garry Kenneth but Zaluska did well to cut out Driver's cross which was bound for Obua.
Moments later, Christophe Berra shot into the side-netting after United failed to clear a corner.
Conway then came close at the other end with a volley after good work by Jon Daly but Marius Zaliukas managed to block the ball for a corner.
Obua's first touch then let him down in front of goal after Aguiar looked to have set up a clear-cut chance.
Hearts looked more and more dangerous as the game wore on with Kingston and Aguiar increasingly influential.
Driver had a great opportunity after a mistake by Dixon but directed his shot straight at Zaluska when he only had the goalkeeper to beat.
Daly sent a strong header a yard wide from a corner as United showed that Hearts were not getting things all their own way.
The striker tested Janos Balogh again in the closing stages from a Conway free-kick but the goalkeeper was alert to the situation as the game finished goalless.