Rangers lost two dreadful goals in the space of two minutes midway through the first half and ultimately they cost them the game.
Getting a goal back quickly settled them down a little bit but in the end it was a costly defeat.
As ever Hearts were full of energy and purpose as they really imposed themselves on Rangers, who found little time or space to get their passing game going.
And Rangers were undone in 20 minutes from a set piece when the defence failed to deal with Bruno Aguiar’s free kick from the left side of the box.
The ball broke to Marius Zaliukas who stabbed it into the net to the fury of the Rangers bench.
Two minutes later as Rangers were caught out again. Once more Aguiar delivered from the left, Christophe Berra headed the ball back across goal and Laryea Kingston forced the ball home.
It was a nightmare start for Rangers but, crucially, they managed to haul themselves back into the game in 26 minutes – also from a set piece.
Lee Wallace fouled Kyle Lafferty and Charlie Adam whipped the ball in from the right hand side. Kris Boyd went to meet it and his effort came off Christos Karipidis and diverted into the net.
It was a lifeline for Rangers who had been second best until that point and continued to find themselves under pressure.
The fire and enthusiasm of Hearts was proving difficult to match and Walter Smith must have been pleased for the half-time whistle to sound so he could get his troops regrouped.
He made an early switch bringing on Chris Burke for his first appearance of the season in 56 minutes, taking off Adam.
It gave Rangers better balance with Burke playing on the right and Lafferty moving to the left and they enjoyed better possession.
However, they could not really create anything of note with the final ball invariably letting them down.
Mendes had a shot over the bar and Bougherra had a header deflected for a corner but Hearts held on stoutly.
Burke’s trickery proved too much for Wallace in 70 minutes when he brought the winger down to earn a yellow card.
Six minutes later and he was sent off for the same offence which put Hearts under real pressure for the final phase of the game.
By this point Novo had replaced the ineffectual Darcheville as Rangers sought to get something from the game.
Rangers forced a free kick and three corners in succession but they could not make any of them pay and time was running out.
With eight minutes remaining Boyd came close when he tried to latch onto Lafferty’s knockdown after Whittaker had crossed from the left but he fired over the top.
Rangers threw everything at Hearts in the final moments but they could not find a way through.