A first-half trio of goals from Charlie Telfer, Scott Fraser and Tony Andreu sank Queens, who were spirited in the second stanza and threatened a comeback with Stephen Dobbie and Derek Lyle on target.
Not since United were defeated on penalties by Stenhousemuir in 1995, the last time they spent a season outside the top-flight, has the club appeared in the final of the Challenge Cup
But the Tannadice men will face Championship rivals St Mirren or Welsh Premier League champions The New Saints at the end of next month after prevailing at Palmerston.
United boss Ray McKinnon said: “We’re glad to be through, although a wee bit disappointed with the second-half performance when we dipped. Queen of the South are a strong side and they came at us after the break so we had to show a lot of character and we did that to deal with them.
“The main objective was to get to the final and I’ll be interested to watch the other semi-final tomorrow.”
The Terrors, who had been somewhat out of form, made four changes as they attempted to kickstart their calendar year following a run of a solitary victory from six matches.
Mark Durnan and Thomas Mikkelsen dropped to the bench with Lewis Toshney and Blair Spittal absent altogether. Sean Dillon returned wearing the captain’s armband and there were also places for William Edjenguele, Telfer and Simon Murray.
If 2017 has been challenging for United then the same couldn’t be said for Queens who are emerging from the gloom of a difficult first half of the season with renewed optimism.
Gary Naysmith, the Doonhamers manager, was forced into three changes with Jamie Hamill, Andy Dowie and young Connor Murray replacing Scott Mercer, John Rankin and Joe Thomson.
However, the former East Fife boss may have been reviewing his options on the bench after his side went 2-0 down inside the opening 11 minutes. Both goals were a result of shocking defending. The opener, in the fourth minute, came courtesy of Telfer’s low strike after Queens made a hash of attempting to clear their lines.
Worse was to follow for the Dumfries men. A clearance from Dowie struck Chris Higgins who then failed to win a tackle, with Fraser helping himself to the loose ball and sending it flying past keeper Lee Robinson.
That United plundered a third goal before the interval came as no surprise. There was a breezy air about their forward play with Queens’ defence lacking in organisation.
Hitman Murray, on the right flank, spotted Andreu lurking with intent on the edge of the box and his subsequent pass was despatched by United’s top scorer into the far corner of the net.
Game over? Well, not quite. Queens were recharged and reinvigorated following the break and reduced the deficit in the 51st minute.
It was Dobbie, their’ most lethal weapon, who popped up with a low strike into the bottom corner after space opened up in front of him on the left-hand side of the area.
But profligacy in front of goal could not be afforded and, on the hour, that was what Queens were guilty of. Dobbie, of all people, spurning the chance to make it 3-2.
Full-back Jordan Marshall’s run into the box ended with a cross which missed everyone and rolled into the path of Dom Thomas. The on-loan Motherwell winger’s shot lacked accuracy but wasn’t dealt with by United. The loose ball was ripe for the back of the net only for Dobbie to blast over from six yards.
Queens set up a grandstand finish when Lyle netted in the first minute of injury-time but United hung on.
Naysmith admitted: “We lost poor goals and gave ourselves too much to do but the second half was a lot better.”