The Tangerines had drawn four times in a row leading into the home clash at Tannadice Park and came through with the goods to move up to seventh on the table, joining Motherwell on 24 points.
The Steelmen had few chances and were unable to grab a leveler only to see Dundee United double their advantage in the final minute of regular time through David Goodwillie who scored his 11th league goal of the season with a neat finish.
Dundee boss John Houston said it was great to see his young players perform so well, praising their influence on the result.
"Johnny Russell scoring was so well deserved because he put in a great shift. The boy has a great chance in the game," he said.
"He is not even playing in his best position yet because he was a right good striker and a good goalscorer through all the youth teams.
"It was great to see a young lad like Stuart Armstrong come on and be positive, driving forward into the box, and one where I thought he was going to pull the trigger, he laid Goodie in, who showed good composure and a great finish.
"It wasn't Goodie's best night but I thought if you keep him on the park, he is liable to score a goal, and he did."