The hosts' victory keeps the race for third place just about alive, with Hearts currently 12 points ahead of United having played one more match.
Diminutive forward Russell scored with a looping header in the 83rd minute and was then presented with an easy tap-in during injury-time as the visitors chased the game.
Peter Houston's United side came under early pressure as Hearts pressed high up the pitch, and Ian Black had a left-footed shot from long distance comfortably held by Dusan Pernis.
Such were United's personnel problems, captain and striker Jon Daly filled in as a centre-half alongside Sean Dillon.
The hosts began to exert an influence on the game and Russell's looping header bounced on the top of the net following Keith Watson's cross.
In a scrappy opening, Hearts registered the next shot on goal. Paul Dixon's poor defensive header from Marian Kello's long kick was picked up by Ryan Stevenson and his shot on the stretch from 18 yards forced a diving save from Pernis.
Referee Iain Brines then had a word with David Goodwillie after the United striker pushed Andy Webster following a tangle.
The official then showed Ismael Bouzid a yellow card for a crunching tackle on Barry Douglas beside the technical area, a decision which Hearts manager Jim Jefferies contested, earning him a talking-to from Brines.
A misplaced Lee Wallace pass was the source of Hearts' next attack as the stray ball was flicked into the path of David Templeton by the alert Ryan Stevenson and the winger crashed a low drive against the advertising boards.
Hearts goalkeeper Kello kept the score level in the 34th minute with a brilliant save to deny Goodwillie.
The Scotland international raced on to meet Douglas' flick and powered a shot towards goal that the Slovakian did well to flick over.
Templeton's mazy run took him into the United box where he found Stephen Elliott, but the Irishman's left-footed shot on the turn bounced past the post.
Hearts right-back Bouzid was lucky to still be on the pitch after 52 minutes when he gave away another foul on Douglas by the corner flag, Brines deciding not to show the Algerian a second yellow card.
It was no great surprise when Jefferies decided to bring on Andy Driver to replace Bouzid moments later, with Craig Thomson dropping back to defence on the right flank.
Sublime close-ball control from Templeton saw him make his way into the penalty area after beating Keith Watson and Morgaro Gomis. The winger fell after a challenge from behind by Watson but referee Brines waved away appeals for a penalty.
Moments later Thomson's delivery from the right found the unmarked Stevenson but he headed well wide.
United midfielder David Robertson drilled a low right-footed half-volley through a crowd of players from outside the box but Kello got down well to the shot.
As the fog that descended on Tannadice worsened, United were stepping up their bid to find the breakthrough goal.
Goodwillie did well to create room cutting in from the left and his near-post shot was pushed behind by Kello.
The marksman then let frustration get the better of him as he appeared to catch Black with his flailing arm in an off-the-ball tussle that was witnessed by the referee, but Brines only decided to caution Goodwillie.
United made the breakthrough with seven minutes left through Russell after his header from substitute Danny Swanson's cross flew over Kello into the back of the net.
Russell added a second in injury-time, prodding home a Paul Dixon cross that was flicked on by Swanson.