At the end of a frustrating week national coach Berti Vogts came to Tynecastle to study Scottish players and ended up watching two Irishmen steal the show.
Danny Griffin gave United a first-half lead with a superb curling free-kick from 25 yards and after Hearts had drawn level substitute Andy Kirk scored the winning goal with 13 minutes left.
The result keeps third-placed Hearts ahead of Kilmarnock in the race for a UEFA Cup spot with United still second from bottom, and also gave home manager Craig Levein revenge on United boss Ian McCall who had masterminded Hearts Scottish Cup exit back in January while in charge of Falkirk.
The game had begun with former Hibs star Russell Latapy being booed by the home support but the United midfielder almost got his own back within the first four minutes when he shot narrowly wide and then created a chance which Andy Tod headed over.
In their first match for almost a month Hearts finally got their act together with Scott Severin and Phil Stamp improvising a clever free-kick and top scorer Mark De Vries guiding a header over the bar.
Jean Louis Valois produced the first effort on target in the 31st minute and United's Scotland keeper Paul Gallacher then had to make an even better save to deny De Vries.
Griffin's wonder strike would have knocked the stuffing out of most teams but Hearts finished the first half strongly and kept pushing after the break as Stamp again brought the best out of Gallacher with a left footed half-volley.
The substitution of Latapy after 57 minutes did the visitors no favours and with Hearts now running the midfield the equaliser came midway through the half when a low cross from Neil Janczyk was hammered home at the back post by defender Andrew Webster.
Hearts went all out for the win and after Gallacher had thwarted substitute Steven Boyack, Kirk pounced on a deflection to grab his 11th goal of the season.