It was the visitors who mastered the blustery conditions early on and Christian Nade was causing problems for the home defence.
It took a fine point-blank save from keeper Graeme Smith to deny him after only two minutes, before moments later the big striker fired over from 12 yards out.
When Hearts opened the scoring on 12 minutes no-one was surprised although there was a hint of controversy around the goal. David Clarkson went down with a head knock and the ref played on. He also waved away a Nade handball as the ball broke to Eggert Jonsson.
Jonsson's shot from 20 yards looked to be soaring wide until Motherwell defender Stephen Craigan stuck out a leg to slice the ball past his own keeper.
The remainder of the first half turned into more of a midfield battle as the wind and the pitch continued to cause problems for both sides.
Hearts also started the second half the better side as they forced four early corners, none of which caused the home side any major alarms.
Fifteen minutes in Hearts were presented with a great opportunity when Craigan upended Lee Wallace at the edge of the box, but Calum Elliot fired the free-kick well over.
Motherwell forced their first corner in the 66th minute, but Marc Fitzpatrick could only head Ross McCormack's inswinging kick wide when he could have been expected to at least have hit the target.
The home side took a lift from this and Steve Banks was forced to make two great saves to keep his side ahead.
Firstly, turning a McCormack free-kick round the post and, from the resulting corner, saving from Marc Fitzpatrick from close range.
With five minutes to go Banks was once again the Jambos hero as he once again denied McCormack with another full-length save from a stinging free-kick.