Gauld's double and goals from John Rankin and Andy Robertson ensured the visitors claimed all three points at Fir Park as United moved two points behind Motherwell in the Scottish Premiership.
Motherwell had the first clear-cut chance of the game after 12 minutes but Stephen McManus' close-range header was deflected over the bar.
Three minutes later, Adam Cummins picked up the game's first booking after barging into Gauld just outside the area.
Motherwell keeper Gunnar Neilsen parried the ball from the resulting free-kick but Gauld, who returned to the line-up after missing United's draw against Celtic, was on hand to slot the ball into the bottom left-hand corner.
United almost extended their lead moments later through Nadir Ciftci whose right-footed effort was palmed away by Neilsen.
But they didn't have to wait long to double their lead when Rankin bundled the ball in from the resulting corner to give United a two-goal cushion
John Sutton tried to hit back late in the first half with a right-footed shot but his effort, which looked destined for the bottom right-hand corner, was saved by United goalkeeper Radoslaw Cierzniak.
United made a bright start to the second-half with John Souttar firing just wide of Neilsen's left-hand post.
Shortly after, Robertson's shot from outside the area rattled the crossbar with Neilsen stranded.
The visitors made it 3-0 after 63 minutes when Gauld got his second of the game. He latched on to a Ciftci pass to the left of the Motherwell goal before firing into the right corner from a tight angle.
Ciftci, returning to the side following a successful appeal against a suspension, almost got on the scoresheet himself after 65 minutes but his shot from range was turned over by Neilsen.
Brian Graham and David Goodwillie had chances late on but Dundee United were not to be denied a fourth when Robertson smashed the ball into the top left corner from distance.
The result keeps Dundee United sixth in the Scottish Premiership.