Carl McHugh was red-carded for a lunge on Don Cowie early in the second half.
Hearts went ahead when Alexandros Tziolis' shot took a deflection off Keith Lasley and looped over goalkeeper Craig Samson.
And Esmael Goncalves struck twice late on, the striker scoring his first goals for the Tynecastle club.
Goncalves had an early low shot just wide before Louis Moult's header hit the bar, but the flag was up - wrongly - for offside against the Motherwell striker.
The hosts had started the match with a back three in an attempt to stymie the Hearts attack, but as the half wore on the away side became more dangerous.
First, a great run from left-back Lennard Sowah forced a save from Samson.
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Then Jamie Walker threatened with a couple of fierce efforts which were just off target. He perhaps should have had a penalty when it looked like he had his shirt pulled in the box.
Malaury Martin then stung the palms of Samson with a free-kick from 25 yards, but Motherwell would finish the half strongly.
From a corner Lionel Ainsworth fired in a shot which was cleared off the line by Anastasios Avlonitis. McHugh then fired an effort over the bar.
Moult was wrongly awarded awarded a free-kick at the edge of the box, having actually been tripped by team-mate Ainsworth. Referee Andrew Dallas even mistakenly booked Hearts midfielder Martin.
Moult took the free-kick himself and the ball flew narrowly wide of Jack Hamilton's goal.
Red cards defined Motherwell's match with Rangers last weekend and another sending off played a massive part in this match.
This time it was McHugh who lunged in, catching Cowie painfully. There were echoes of Scott McDonald's red card tackle on Rangers' Kenny Miller, and it looked like the right decision by Dallas.
Just minutes later Hearts opened the scoring. The impressive Greece international midfielder Tziolis fired in a shot from 20 yards which took a massive deflection off Lasley and beat Samson.
But Lasley almost levelled moments later, his effort narrowly off target.
Goncalves has shed 8kg and with his improved conditioning and professionalism it's intriguing to ponder what he can do for this Hearts side.
The management at the club clearly believe in the talents of this mercurial player, and that belief will give Goncalves added confidence.
He looked determined to get his first Hearts goal and caused Motherwell problems all afternoon.
It finally came as he fired home with a composed finish. It clearly meant a lot to him as he celebrated with the travelling fans - for which he was duly booked.
Goncalves restrained himself from a second yellow after he scored again as Hearts made it two wins in four days following Wednesday's 4-1 defeat of Rangers.
Match ends, Motherwell 0, Heart of Midlothian 3.
Second Half ends, Motherwell 0, Heart of Midlothian 3.
Attempt missed. Sam Nicholson (Heart of Midlothian) right footed shot from outside the box is just a bit too high.
Attempt blocked. Sam Nicholson (Heart of Midlothian) right footed shot from outside the box is blocked.
Goal!  Motherwell 0, Heart of Midlothian 3. Esmael Gonçalves (Heart of Midlothian) right footed shot from the centre of the box to the centre of the goal. Assisted by Moha.
Lennard Sowah (Heart of Midlothian) wins a free kick on the left wing.
Foul by Jack McMillan (Motherwell).
Attempt saved. Esmael Gonçalves (Heart of Midlothian) right footed shot from the centre of the box is saved in the centre of the goal.
Esmael Gonçalves (Heart of Midlothian) is shown the yellow card for excessive celebration.
Goal!  Motherwell 0, Heart of Midlothian 2. Esmael Gonçalves (Heart of Midlothian) right footed shot from the right side of the box to the bottom right corner. Assisted by Moha.
Attempt blocked. Esmael Gonçalves (Heart of Midlothian) right footed shot from the centre of the box is blocked.
Moha (Heart of Midlothian) wins a free kick in the defensive half.
Foul by Zak Jules (Motherwell).
Andraz Struna (Heart of Midlothian) wins a free kick in the attacking half.
Foul by Lee Lucas (Motherwell).
Substitution, Heart of Midlothian. Sam Nicholson replaces Jamie Walker.
Attempt saved. Esmael Gonçalves (Heart of Midlothian) right footed shot from outside the box is saved in the centre of the goal.
Attempt blocked. Esmael Gonçalves (Heart of Midlothian) left footed shot from the centre of the box is blocked.
Esmael Gonçalves (Heart of Midlothian) wins a free kick in the defensive half.
Ben Heneghan (Motherwell) is shown the yellow card for a bad foul.
Foul by Ben Heneghan (Motherwell).
Foul by Esmael Gonçalves (Heart of Midlothian).
Stephen McManus (Motherwell) wins a free kick in the defensive half.
Attempt missed. Esmael Gonçalves (Heart of Midlothian) right footed shot from the centre of the box is close, but misses to the right.
Attempt missed. Keith Lasley (Motherwell) right footed shot from outside the box is close, but misses the top left corner.
Foul by Jamie Walker (Heart of Midlothian).
Keith Lasley (Motherwell) wins a free kick in the defensive half.
Substitution, Heart of Midlothian. Perry Kitchen replaces Malaury Martin.
Goal!  Motherwell 0, Heart of Midlothian 1. Alexandros Tziolis (Heart of Midlothian) right footed shot from outside the box to the high centre of the goal.
Attempt blocked. Moha (Heart of Midlothian) left footed shot from outside the box is blocked.
Corner,  Heart of Midlothian. Conceded by Stephen Pearson.
Substitution, Motherwell. Stephen Pearson replaces Lionel Ainsworth.
Substitution, Motherwell. Lee Lucas replaces Steven Hammell.
Don Cowie (Heart of Midlothian) wins a free kick in the defensive half.
Carl McHugh (Motherwell) is shown the red card.
Foul by Carl McHugh (Motherwell).
Alexandros Tziolis (Heart of Midlothian) wins a free kick in the attacking half.
Foul by Louis Moult (Motherwell).
Corner,  Heart of Midlothian. Conceded by Ben Heneghan.
Second Half begins Motherwell 0, Heart of Midlothian 0.
Esmael Goncalves scored twice as Hearts overcame 10-man Motherwell in Saturday's early Scottish Premiership match.