Keith Lasley's deflected shot off Hearts defender Andy Webster and a Jamie Murphy header gave the Steelmen the interval advantage.
Home skipper Lasley was sent off five minutes after the break for picking up a second yellow card, both of which were for fouls on midfielder Ian Black.
Motherwell shrugged off the numerical disadvantage and midfielder Nicky Law finished off a fine move in the 65th minute by driving past Jamie MacDonald to seal the win which became more significant with the news from Ibrox.
Rangers' 1-0 defeat by Kilmarnock means Motherwell moved to six points behind the champions - this week deducted 10 points for entering administration - with a game in hand which promises an interesting battle ahead.
Defender Tom Hateley shrugged off an illness to take his place in an unchanged home side.
Hearts made four changes, with Ryan McGowan, Ian Black, David Templeton and Andrew Driver coming in for suspended Jamie Hamill and Mehdi Taouil, Scott Robinson, and Rudi Skacel, who all dropped to the bench.
Motherwell took the early initiative but Hearts goalkeeper Jamie MacDonald put his own side under pressure in the fourth minute when he spilled a rather ordinary-looking Hateley cross from the right.
However, MacDonald made amends instantly by saving Henrik Ojamaa's low drive from the loose ball before making another block from Steve Jennings' effort.
The visitors edged their way back into a game but it turned into a scrappy midfield battle with neither goalkeeper seeing much action in the opening quarter.
In the 24th minute Lasley was booked for a heavy challenge on Black which gave both sets of fans something to shout about.
Templeton fired over the bar from 25 yards in the 31st minute, seconds before Ojamaa drove a great ball across the Hearts goal at the other end from the right side of the box, only to find no takers.
The match was warming up, though.
McGowan went close four minutes later when he forced his way past Tim Clancy and into the Motherwell box but his angled drive sped past the far post.
The game sparked into life in the 37th minute when Motherwell made the breakthrough.
The Hearts defence failed to properly clear Hateley's corner from the left and MacDonald was forced to make a good save from Murphy's close-range drive after the ball fell to his feet.
However, the ball rebounded out to Lasley and he fired it straight back in at goal where it appeared to come off Webster before hitting the back of the net.
In the 41st minute, following a good passage of play by the home side, Murphy headed Lasley's cross in off the crossbar and a game that was going nowhere at one point was firmly in the hands of the Steelmen.
Robinson replaced Driver for the start of the second half which began with Webster making a mistake inside his own box, allowing Ojamaa a chance to make it 3-0, but again MacDonald came to the rescue with a good block before Law knocked the rebound over the bar.
The match took another twist in the 51st minute when Lasley was shown a second yellow card and dismissed by referee Alan Muir for another foul on Black, leaving the home side down to 10 men and their supporters incensed.
However, it was the home side who threatened a few minutes later when Law chipped just over the bar from 25 yards after MacDonald was forced out to the left-hand side of his box to thwart Murphy, who had raced clear.
In the 55th minute Law went even closer with a fine strike from a similar position which crashed off the crossbar.
Black was then booked for a foul on Ojamaa which delighted the home fans who had more to celebrate moments later, in the 65th minute, when Law made it 3-0 with a well-worked goal.
Ojamaa went past several Hearts defenders before laying the ball off to Murphy who helped it on to the on-rushing Law and he cracked a low drive past MacDonald and in off a post.
Black was replaced by Taouil to the delight of the home fans who watched their side play at times as if they had the man advantage.
Hateley fired a free-kick from wide on the left inches over the bar in the 78th minute as the visitors slowly ran out of steam and belief.
In the 86th minute more good work from Ojamaa on the left ended when he fired the ball to the back post where striker Michael Higdon allowed it go under his foot with the goal gaping, although the flag might have been raised had he put the ball in the net.
In the end it was a comfortable win for the 10 men who can now train their sights on Rangers in the weeks ahead.
