Peter MacDonald's hat-trick helped Morton cut the gap at the top of the First Division to just two points following their 5-2 win over bottom club Airdrie.
With leaders Partick not playing, Allan Moore's men took full advantage to move to within striking distance before Wednesday's top-two clash.
MacDonald grabbed his first in the fifth minute, turning in Colin McMenamin's cross, and duly added a second in the 22nd minute with a low drive from 12 yards.
He completed his hat-trick with a stunning strike into the top corner from 25 yards.
McMenamin added the fourth from the penalty spot after Grant Evans fouled Mark McLaughlin, before Airdrie pulled one back when Sean Lynch thumped in from close range.
Alan Cook prodded home William McLaren's cross in to make it 4-2 but, after United had Grant Evans sent off for a professional foul on Archibald Campbell in the 80th minute, Marc Warren headed into his own net to restore the three-goal cushion.
The visitors remain 10 points adrift at the bottom after a 10th game without a win.