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, but Stuart McCall's side held on to cement second place in the league and condemn the Tynecastle side to their fifth-straight loss.
Inverness Caledonian Thistle slipped three points behind Well after they were held to a goalless draw at Ross County, who stay a point behind Caley in fourth.
Chances were few and far between throughout the 90 minutes with neither side able to dictate proceedings at any stage of the match.
Richie Foran drilled across the County goalmouth yet the inrushing Billy McKay just failed to connect in front of goal.
Ivan Sproule raced on to a long through ball from Grant Munro in the 11th minute, only for the move to peter out when Sam Morrow ran out of space.
County came close to an opener in the 24th minute when Evangelos Oikonomou pounced on a Sproule cut back. However, his goalbound shot was brilliantly turned behind for a corner by Inverness goalkeeper Ryan Esson.
The visitors came close in the 29th minute when a Graeme Shinnie corner fell to Ross Draper at the far post but his strike was cleared off the line by Rocco Quinn.
County came agonisingly close to the opening goal five minutes later when Mihael Kovacevic collected a cross-field ball from Paul Lawson, scooped the ball over Graeme Shinnie's head and flashed a shot just inches past the far post.
Owain Tudor Jones scooped the ball over the crossbar after a breakaway move.
County had a chance right at the death when the ball fell for Richard Brittain on the edge of the area yet he blasted high and wide.