A dominant first-half performance from United ensured they made comfortable work of Stranraer.
The Scottish Premier League side made the trip to Stair Park keen to avoid a potential upset and never looked in any danger as Russell's hat-trick and a brace from Jon Daly secured a routine win.
It was the first time the two sides had met since August 2004, when the Tannadice side won 3-1. Stranraer featured Stevie Aitken that day and he took charge of the home side as they welcomed the SPL club.
United scored their opener in the 13th minute as Barry Douglas' cross took a kind deflection off right-back Mark Staunton and fell kindly to Russell. The striker then hit it first time to bury it between David Mitchell and the near post from just six yards.
They added a second on 26 minutes and again Douglas and Russell were involved. The left-back again pushed forward and whipped the ball in where it was controlled by Rudi Skacel. Last year's cup winner, with Hearts, then squared it to Russell who turned his man and rolled the ball into the bottom left corner.
Any chance of a comeback looked remote and was surely extinguished before the break. Once again the ball came from the left but this time it was Russell's strike partner Jon Daly who scored.
The home side could not clear their lines and after Russell was denied it came to Daly to bury it from close range.
In the second half Daly grabbed his second on 61 minutes. This time it was a corner from the left and when the hosts failed to clear the striker was lurking to bundle it home.
It looked like being a long day for Stranraer when Russell completed his hat-trick just moments later. Mitchell blocked substitute Michael Gardyne's low angled shot with his legs but the striker rattled in the rebound from the edge of the 18-yard box.