Trailing to a first-half own goal from captain Stephen Craigan, Stuart McCall's side battled back and missed a string of chances before Higdon struck in the 85th minute.
It ends a run of three successive defeats for the Fir Park side, but they still dropped down to fifth place after St Johnstone beat Hibernian.
Dundee United are still searching for their first victory of 2012 but the draw moved them back into the top six.
United manager Peter Houston made just one change to the side that lost 2-1 to Celtic last weekend, with Stuart Armstrong replacing Willo Flood.
Motherwell manager McCall also made just one change after the 1-0 home loss against Inverness Caledonian Thistle. Steve Jennings returned for Tim Clancy.
The visitors had the first chance in four minutes when Tom Hateley's curling free-kick was parried by Dusan Pernis. United defender Garry Kenneth cleared the loose ball.
Gary Mackay-Steven has been in fine form for United in recent weeks and was unlucky with a rising drive in the sixth minute after showing sublime skill.
Omar Daley, using his pace to good effect on the right side of a 4-3-3 formation, tested Pernis with a low drive on 15 minutes.
United settled and captain Jon Daly missed a great chance after being picked out at the back post by Stuart Armstrong. Towering above Steven Hammell, he headed over the bar.
Motherwell striker Michael Higdon had been quiet yet almost broke free to convert Nicky Law's cross midway through the first half - but Pernis' fingertip save denied him.
Within seconds, Motherwell goalkeeper Darren Randolph bettered that save with a stunning stop from John Rankin's stinging drive, after great play from Daly and Mackay-Steven.
However, there was nothing the Irishman could do to prevent United taking the lead in the 28th minute, with Craigan yet again the unfortunate fall guy.
Paul Dixon was the provider with a wonderful left-wing run and his low cross was bundled over the line by the Motherwell captain, under pressure from Johnny Russell.
Replays showed that Craigan did get the final touch to Dixon's cross, leaving him with the unwanted record for the most own goals in the SPL with eight.
Despite that setback, Motherwell continued to create chances. Keith Lasley's long-range drive was held by Pernis, while the Slovakian also denied Higdon after great work from Jennings.
United hit back and Randolph made a good save from Russell's low shot, while Daly also missed a good chance after a swift United breakaway.
The impressive Mackay-Steven then danced away from three challenges and flashed a drive into the side-netting in 40 minutes.
The second half was nowhere near as open as the first, with chances extremely scarce after the break.
Daley was well shackled by Paul Dixon and it was no surprise when he was taken off for Henrik Ojamaa just after the hour mark.
The Estonian had only been on the pitch for seconds when Motherwell carved out an opening, but Jamie Murphy's low drive was expertly gathered by Dusan Pernis.
Ojamaa's pace and trickery earned a free-kick for Motherwell in the 66th minute but Steven Hammell's curling effort drifted narrowly wide.
United's Robbie Neilsen, booked in the first half, was walking a tightrope and Houston wisely replaced him with Gavin Gunning.
Motherwell were starting to pin United back and Higdon was inches away from connecting with Nicky Law's cross in the 69th minute.
Higdon wasted another good chance in the 77th minute when he headed Tom Hateley's cross wide from just six yards.
However, United could have extended their lead as Russell blazed over and Randolph saved smartly from Daly.
Higdon was having a hard time for Motherwell and fired a wayward shot into the stand after great play from Ojamaa.
However, his perseverance paid off in the 85th minute when he latched on to Ojamaa's cutback and fired high past Pernis.
Motherwell pressed for the winner and Ojamaa went down under Dixon's challenge in the box, but referee Stevie O'Reilly waved away the claims.