Higdon was the target of abuse from a section of the Fir Park fans as Motherwell laboured to a 1-0 win over Aberdeen last weekend but he bounced back to net in each half as Motherwell cruised to victory.
The former St Mirren striker punished a poor clearance from Dundee United goalkeeper Dusan Pernis in first-half injury-time before taking his tally for the season to six with a 64th-minute penalty.
Stuart McCall's side never looked back after the impressive Keith Lasley applied a superb first-time finish to a cutting 13th-minute move and they held on comfortably after Jon Daly's consolation. Motherwell won the midfield battle with Lasley's energy and enthusiasm smothering the home side alongside the composed Steve Jennings, with Nicky Law breaking to good effect.
United's creative players failed to shine with Danny Swanson struggling to produce anything of note following his Scotland call-up.
United carved out the first chance when Ryan Dow, in for Johnny Russell, crossed for Jon Daly, whose header was held by Darren Randolph in the Motherwell goal.
But Motherwell were already enjoying a lot of the ball and they went ahead following a slick move.
Law's pass found the unchecked overlap of Tom Hateley and the right-back drove the ball into the box, where Lasley met it on the run to arrow a powerful strike high into the net from 14 yards.
Motherwell took confidence from the goal and United struggled to get out of their own half before Peter Houston made a 30th-minute change, bringing on on-loan Fulham striker Lauri Dalla Valle for Dow.
United began to force Motherwell back and Dalla Valle headed Keith Watson's cross on target but Randolph again made a comfortable catch.
Daly lobbed over from 25 yards before Motherwell went two ahead in injury time after a blunder by Pernis.
Watson passed the ball back to the goalkeeper, whose kick-out went straight to Higdon. Pernis still had a chance to atone as he got down to meet Higdon's angled left-footed effort, but the Slovakian could not get a strong enough hand to the ball and the shot went in off the post.
Motherwell might have had a penalty just after the break when Gavin Gunning appeared to push Higdon as they challenged for Law's cross, but the striker did not appeal and referee Steven McLean played on.
United put pressure on sporadically but were not seriously threatening.
Stevie Hammell took the ball off Daly's feet after the ball fell for the striker in the box before Tim Clancy diverted Swanson's shot over, with the unmarked Scott Robertson heading wide from the resulting corner.
United appealed for handball as Hateley cleared another corner but Motherwell broke and Pernis had to be quick off his line to stop Lasley converting Jamie Murphy's through-ball.
Motherwell soon extended their lead after Garry Kenneth brought down Law as the midfielder cut in along the byline. Higdon sent Pernis the wrong way from the spot.
Houston brought on Russell and Gary Mackay-Steven for Robertson and Swanson and they finally gave Randolph a serious test when Gunning fired in a powerful 30-yard free-kick which the goalkeeper pushed wide.
United pulled one back in the 77th minute when Daly forced the ball home from close range after Paul Dixon's low cross across the six-yard box had been turned back by Keith Watson.
But Motherwell saw the game out to move second in the SPL ahead of Celtic's Sunday visit to Hearts.