Following last week's derby defeat to City rivals Hibs, it was vital that Hearts got back on track and this win puts them back on top of the premier league.
But in truth it was made easy for them by a woeful United side, who simply failed to compete in midfield where they were overrun.
With all the problems in the past week, Hearts needed to get the fans behind them and Paul Hartley gave them a dream start after only three minutes.
Saulius Mikoliunas did the damage with a driving run at the heart of United's defence and then slipped an inch-perfect pass to Hartley, who provided a cool finish from the edge of the box.
And it was one-way traffic as Calum Elliot came close from 25 yards and then Rudi Skacel forced a fine save from Derek Stillie with a vicious drive.
But the Dundee keeper was badly at fault when Hearts increased their lead after 25 minutes when he allowed Rudi Skacel's floated free-kick to drift in at his right post without a touch.
Hearts continued to dominate for the remainder of the first half, but couldn't add to their goal tally until the 57th minute. Yet again it was defensive suicide from United. Paul Hartley was able to charge down Alan Archibald's clearance, and he headed for the by-line to cut the ball back for Michal Pospisil to bundle the ball home from close range.
The game was dead and buried and Dundee United began to get a few chances, but David Robertson fired wide after the ball broke to him off Robbie Neilson.
Even a penalty couldn't allow Gordon Chisholm's side on to the score sheet. Steven Pressley tripped David Robertson in the box, and Robertson picked himself up to take the spot-kick but was foiled by a great double save from Craig Gordon to emphasise the gulf in class between the sides.