Saturday's result deepened relegation-threatened Hibs' predicament at Easter Road.
After Leigh Griffiths hit the post for Hibs in an even first half, United cut through their hosts twice in quick succession, with Russell netting after 65 minutes before putting Mackay-Steven through for the second with 17 minutes remaining.
Hibs remain with one SPL home win this season and now sit just three points clear of bottom club Dunfermline, who today drew 1-1 with St Mirren, with seven matches remaining.
United play the Pars next week and could aid Hibs' plight, but the capital club must find more quality in the closing weeks of the season to aid their survival fight.
Hibs, who lost 2-0 to Edinburgh rivals Hearts last Sunday, were on Wednesday moved to deny a report Griffiths had headbutted manager Pat Fenlon and punched assistant manager Billy Brown in a training ground bust-up.
On-loan Wolves striker Griffiths, who signed for the Premier League side from Dundee, started in a side showing two changes as Hibs sought to enhance their four-point advantage over the Pars.
Captain James McPake (back) was replaced in defence by Matt Doherty and midfielder Isaiah Osbourne returned from suspension.
United were unchanged following their 2-1 win over Rangers and came close in the opening minute when a Mackay-Steven corner had Hibs in trouble.
The ball squirmed through to Gavin Gunning at the back post and the United defender shot straight at Graham Stack.
Griffiths rattled the frame of United's goal after 10 minutes.
A George Francomb corner found Griffiths at the back post and he struck a fierce shot which beat Dusan Pernis but bounced clear off the post.
Doherty was booked for a foul on John Rankin and from the resulting free-kick Stack turned Jon Daly's header over.
Griffiths shot straight at Pernis and Osbourne failed to get a header on target soon after as Hibs pushed on once more.
A Willo Flood corner found Gunning, who could not connect with a header, and the ball fell for Sean Dillon, who was able only to volley off target.
After a tepid conclusion to the first half, United went on the attack at the start of the second.
Daly twice came close from Mackay-Steven crosses and attacking opportunities were rare for Hibs.
A poor Tom Soares through ball directed towards Griffiths almost caused the visitors a defensive embarrassment as Gunning's sliced clearance went narrowly wide of his own goal.
United responded and Scott Robertson's cross from the right reached Mackay-Steven, whose prod towards goal bounced over Russell and was blocked by Stack as Hibs scrambled clear.
Mackay-Steven then ran at Hibs through the middle of the park, beating three men before shooting narrowly over.
Pernis then was alert to snuff out an opportunity for Hibs as Pa Kujabi's cross from the left found Griffiths, who controlled on his chest, but the United goalkeeper made a crucial intervention.
United took the lead after Daly and Russell combined, with the latter feeding Rankin to shoot. Stack saved with his feet, but Russell, who had continued his run, was the quickest to react and passed the ball into an empty net.
Daly departed after an aerial collision with Hanlon, but it did not have an adverse impact on United.
After 73 minutes, the visitors went two ahead as Russell found Mackay-Steven in the left channel.
The winger burst forward and his shot squeezed under a hapless Stack at the near post.
Substitutes Ivan Sproule and Garry O'Connor then shot weakly at Pernis as United eased to victory.