Meanwhile, the Tangerines are enduring a poor run of form since the turn of the year, failing to win in 2021 and conceding nine goals in their last four matches.
The Staggies broke the deadlock after 14 minutes through Oli Shaw, however second-half strikes from Devante Cole and Bevis Mugabi turned the game on its head, securing the Steelmen their first win in 14 matches in all competitions.
Motherwell remain in a precarious position, one place above the relegation playoff spot, currently occupied by last week's opponents Ross County.
The Steelmen are winless in their last six home league games, the longest ongoing run of all sides in this season's Scottish Premiership. They also lost their last home encounter with Dundee United, which saw the Tangerines seal a narrow 1-0 win back in August.
With a match away at Celtic on the horizon, Alexander will hope to head into that fixture off the back of two positive results and a win on Wednesday would see the Steelmen record successive league wins for the first time since October.
Dundee United will want to quickly move on from last week's misery as a 5-1 thrashing at home to St Mirren was followed by a 2-0 loss to Hibernian on Saturday.
Micky Mellon's side have now failed to win any of their last seven games and as a result have slipped to seventh in the table.
Fears of the drop may start to creep in if their poor run of form continues, however there is an eight-point gap between themselves and 11th-placed Ross County and a few positive results could change their outlook on the season going forward and ease any relegation worries.
One of Dundee United's main concerns is their away form, having won only two of their 12 matches on the road this season, the fewest of any side in the division. They have also found it difficult to score on their travels, finding the net just five times, again the lowest total in the top flight this campaign.
The Tangerines head into their fixture with Motherwell having won six of their last eight Scottish Premiership visits to Fir Park.
Mellon's men have already picked up four points from their two matches against the Steelmen this campaign and a win on Wednesday could move them up one place to sixth in the table, nine points clear of Motherwell.
Motherwell Scottish Premiership form: LLDDLW
Dundee United Scottish Premiership form: LDDDLL
Dundee United midfielder Logan Chalmers is nearing a return from an ankle injury but is not expected to return this week, while defender Declan Glass is likely to be out for the rest of the season with an anterior cruciate ligament injury.
Motherwell possible starting lineup:
Kelly; O'Donnell, Mugabi, Gallagher, Carroll; Campbell, Crawford, Maguire; Long, Cole, Watt
Dundee United possible starting lineup:
Siegrist; Smith, Connolly, Reynolds, Robson; Bolton, Butcher, Harkes, McNulty; Clark, Shankland
We say: Motherwell 1-1 Dundee United
Both sides have struggled to win games this campaign, winning just 11 league matches combined so far. Motherwell will have confidence heading into Wednesday's clash having won last weekend, but they face a Dundee United outfit who they have failed to beat in two attempts already this season. There is not much to separate the two sides and so a draw could be on the cards.