Michael Higdon grabbed his 20th goal of the season as Well's blistering start was enough to secure all three points against Hearts at Tynecastle.
The Jambos' 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 before Dylan McGowan was credited with scoring an own goal when he failed to keep out a Nicky Law effort.
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.
In Saturday's other SPL game, Ross County and Inverness drew a blank in a scrappy Highland derby.
Chances were few and far between throughout the 90 minutes with neither side able to dictate proceedings at any stage of the match.