It took Motherwell only 46 seconds to open the scoring, when Marvin Kaleta reacted quickly to a loose ball, fired a cross in and Stamatelopoulos turned it in from a few yards out.
The lead did not last long. Moult was caught in the box after collecting a cross and, after a video assistant referee review, Dalby stepped up to equalise - and became the Premiership's top scorer in the process.
It took a little longer for the third goal to come and it came from more good work from Kaleta on the right. Twisting and turning, he picked out Harry Paton at the back-post, who in turn found Halliday to turn home from a yard out.
Stamatelopoulos added to the hosts' lead before the break, rising nicely to divert a Tawanda Maswanhise cross.
While Motherwell were clinical at the front, they gifted United a goal in the second half when Oxborough failed to deal with Glenn Middleton's deflected cross, with the ball bouncing off Dalby and in.
The game was almost level when Middleton then picked out Moult in the middle, but his placed effort was turned onto the bar by Oxborough, making amends for his earlier gaffe.
Motherwell breathed a sigh of relief, went up the pitch, and scored. Stamatelopoulos turned creator, laying the ball off nicely to Sparrow who finished cooly with the outside of his foot.
However, it was a nervy final few minutes after Moult powered in a header, but United never came close to another goal.