As was the case in the previous match against Motherwell, a much improved second half performance wasn't enough to earn the Tannadice youngsters a point they probably deserved.
Saturday morning's clash was switched to the Science Park in Glasgow and United just never got going in the first half.
And they could have little complaint about going in at half time trailing to goals from Reid Brown and Daniel McKay after 28 and 33 minutes at the interval.
However, it was different story in the second half and even before Ryan Dow smashed home a terrific free-kick from 25 yards just after the hour mark, both Robert Thomson and John Murray had gone close.
Though continuing to be on top for most of the rest of the game, the best the visitors could create was a half chances.
Indeed, as United threw bodies forward, goalkeeper Connor Grant twice came to the rescue with good saves to prevent the Rugby Park side extending their lead, but that would have been harsh on United's second half endeavours.
Dundee United: Grant, Irvine, Shaw, Lee, Whyte (Leitch 75), Dow, Stokes, Ross McCord, Hilson, Thomson, Murray (L Swanson 70). Subs not used: McCallum, McCulley, Burns, W Robertson.