Hearts' new interim management team of Gary Locke and Darren Murray were taking charge for the first time following manager John McGlynn's departure on Thursday, but their side were left with a mountain to climb after conceding twice in the opening eight minutes.
Higdon swept in the opener for Motherwell before Dylan McGowan was credited with scoring an own goal when he failed to keep out a Nicky Law effort.
Former Motherwell striker John Sutton pulled one back after the break as Hearts put the visitors under pressure, but Stuart McCall's side held on to cement second place in the league and condemn the Tynecastle side to their fifth straight loss.
After admitting that managing Hearts on a permanent basis was his dream job, joint interim-manager Locke had the chance to stake his claim for the vacancy.
But the hosts could not have got off to a worse start.
Just under three minutes were on the clock when Higdon coolly swept a low 18-yard left-footed shot past Jamie MacDonald into the net. The ball came to the towering Englishman after advantage was played when James McFadden had been fouled by Andy Webster.
Hearts tried to respond immediately but Michael Ngoo headed over from a Ryan Stevenson cross.
Higdon then played a part in the visitors' second as Motherwell made a great start to the match.
The forward threaded a ball through to Law, who was afforded space inside the box. His first shot blocked by MacDonald but his second found the net after McGowan could only slice the ball into his own goal on the line.
Hearts were exhibiting all the signs of a team lacking in confidence, a factor that was not helped by moans and groans emanating from the home stands as they failed to get a foothold on the game.
Things started to look better for the Tynecastle outfit, though.
Mehdi Taouil picked up a loose ball 25 yards from goal but his right-footed curling effort sailed over the bar.
Callum Tapping then caused panic with a jinking run towards the edge of the area, before eventually passing to Jamie Walker. The winger's effort from 16 yards fell kindly into keeper Darren Randolph's arms after deflecting off Stevie Hammell.
Motherwell looked dangerous every time they attacked but Webster was on hand to clear the danger after 28 minutes when Higdon played a pass across the six-yard box, having rounded MacDonald.
Randolph pulled off a stunning save in the 34th minute to deny Ngoo. Taouil's diagonal cross was knocked down by Sutton and Ngoo's reverse shot looked goal-bound before the Irishman expertly got down to palm the ball clear.
Stevenson's snap-shot from close range was shanked well wide following an Adam Cummins tackle on John Sutton.
Arvydas Novikovas replaced Tapping at the break and the Lithuanian was involved in setting up Hearts' next chance seconds after the restart.
The winger's flick created a gap for Stevenson to drive into but the midfielder's tame shot was easily collected by Randolph.
Hearts dragged themselves back into the contest in the 59th minute, however, when Sutton headed in against his old club.
Motherwell felt aggrieved they were not awarded a throw-in on the halfway line and Novikovas earned a corner.
Sutton flung himself at the substitute's set-piece from close range to find the net.
Hearts piled on the pressure and Stevenson had a shot from a tight angle blocked by Randolph before Webster's left-footed half volleyed bounced just wide, but they fell short in the end.
- Sports & Recreation