And this hard-fought 2-1 triumph at Tannadice became the third scalp on opposition soil in recent weeks to reinforce Well's reputation as the SPL's away-day specialists.
Given that Stuart McCall's men took four points from a possible six at Tannadice last season, the journey north was always likely to throw up a positive result for the visitors.
The stringing together of a three-game unbeaten run, since United caught Well with a late Johnny Russell strike three weeks back, fails to follow the trend that has seen Motherwell claim just seven points at home from a possible 28, a record that has blighted Well's early bid to repeat last season's Champions League heroics.
Needless to say Well boss Stuart McCall's pre-match mood would not have been helped by the two-game ban tabled by the SFA Compliance officer for violent conduct by keeper Darren Randolph in the wake of his high challenge on Hearts' Callum Paterson last time out.
Yet it did not take long for McCall's air to lighten.
In a league in which the importance of drawing first blood can't be underestimated, it was Well who hit first and hard with just seven minutes gone.
Tom Hateley's fine right wing cross amazingly eluded three dreaming Tangerine defenders and Michael Higdon cooly dispatched the ball form eight yards passed the helpless Radoslaw Cierzniak.
Three minutes later it was two. Henrik Ojamaa picked out Chris Humphrey with a stunning right-foot diagonal pass and the Jamaican internationalist hardly broke his stride to smash home a 25-yard rasper.
But in 37 minutes United found a way back into the game when Jon Daly latched on to a Sean Dillon cross before smashing home a rising drive from 16 yards out as the home side began to test Well's mettle.
The visitors almost regained their two-goal advantage when Higdon's 30-yard snap shot was brilliantly pushed over by Cierzniak.
But with United responding to Houston's half-time team talk, Rudi Skacel should have levelled things just before the hour mark when he swivelled inside the box, but he rifled his effort over.
Then in 79 minutes Well hit on the counter and only a brilliant save from Cierzniak denied Jamie Murphy a third for the Lanarkshire side.
With skipper Keith Lasley the epitome of composure in the visiting midfield, and Murphy and Ojamaa threatening on the counter, Well remained calm under fire.
Although the hosts continued to tighten their grip on the game, Motherwell's young centre-back pairing of Adam Cummins and the impressive Shaun Hutchinson held firm to help their side's unbeaten run stretch to four games.
While Well boss McCall can take comfort from the maturity being shown by his kids at some of the country's most testing venues, the Fir Park manager will know that with every success they continue to help register, the chance of him retaining their services, and especially that of the imposing Hutchinson, recede.
As much as Motherwell suffered a trying sequence of results around the festive period last year, the Fir Park side showed a determination within their ranks that bodes well for the season ahead.
While this bruising victory will have provided the ideal platform into Saturday's William Hill Scottish Cup trip to Aberdeen.
Meanwhile, Dundee United chairman Stephen Thompson has resigned from the SPL board, citing "professional differences".
His departure follows that of chairman Ralph Topping, who will leave his post before the end of the season.
The other board members include chief executive Neil Doncaster, Celtic's Eric Riley, Duncan Fraser of Aberdeen and Kilmarnock chairman Michael Johnston.