A Gavin Gunning header after 14 minutes put Peter Houston's men ahead before Russell netted twice in three minutes just before the break to give the Terrors an unassailable lead.
Both sides had to play the final 20 minutes with 10 players after Russell and Dundee captain Stephen O'Donnell both saw red for violent conduct. The win moved United to the top of the Clydesdale Bank Premier League as they maintained their 100% record, while Dundee were left still looking for their first victory and goal of the new campaign.
The game started at a frantic pace with a Michael Gardyne shot bravely blocked by Dundee defender Matt Lockwood before Nicky Riley was twice denied at close range by United stopper Radoslaw Cierzniak with less than five minutes played.
However it was United who broke the deadlock after 14 minutes when Dundee goalkeeper Rab Douglas came to collect a Willo Flood free-kick but made no connection, giving Gunning the easiest of tasks to head the ball into the unguarded net at the back post.
The Dark Blues were pressing for an equaliser but were almost caught on the counter when the unmarked Gardyne cut the ball back for John Rankin but the midfielder's acrobatic effort drifted harmlessly wide.
However, United were to double their advantage 10 minutes before the break when Rankin threaded a perfect pass into the path of Russell, whose shot looked to be heading wide before a deflection off Italian defender Davide Grassi took the ball past the helpless Douglas.
And Russell extended the United lead with a spectacular strike three minutes later. The forward collected the ball from Barry Douglas before cutting inside and unleashing a venomous shot from 25 yards which flew into the net.
Douglas went some way to redeeming himself with two fine stops after the break, clawing away a Richie Ryan drive before getting down well to keep out a Jon Daly header as United's dominance continued.
Both teams had to play the final 20 minutes a man short after a tackle between Dundee skipper Stephen O'Donnell and Russell sparked a melee between both sets of players and when order had been restored the two players were given their marching orders by referee Calum Murray.
Source: PA
Source: PA