Two goals from Ryan Gauld and one each for Paul Paton and Andy Robertson saw the visitors to victory but they were helped considerably by poor defending from a makeshift home rearguard.
Motherwell, looking to extend their winning home run to six consecutive games, had to do so with three changes in their back four with the ever-present of trio of Simon Ramsden, Stevie Hammell and Shaun Hutchison missing through injuries and suspension.
However, the 'Well boss refused to use the excuse of missing the trio of defenders and admitted his men were well beaten.
He said: "You don't want to lose at home by that margin but in all my time here that was the best performance of any visiting team and I include Celtic, Rangers and European opponents in that.
"Sometimes you have to hold your hands up and say you were well beaten.
"I said at the start of the season that they had a good, young squad and they came here on the back of a couple of impressive away displays.
"We just have to lick our wounds and take it on the chin."
The 'Well boss did point out his side's defensive deficiencies which made United's task a little easier, saying: "United are a great team from middle to front and they were possibly the worst opposition to face with an inexperienced defence.
"I can't be too critical of the players but we might have defended the first two goals better and for the third Stuart Carswell is missing from the area they scored.
"But I don't want to make excuses and the scoreline was a fair reflection of the game."
Opposite number Jackie McNamara was understandably delighted and said: " I thought we played very well against Celtic last week without taking our chances.
"Today I thought we created as many chances and the only worry I had was that we only had a two goal lead at half-time.
"Motherwell were on a great run at home and we knew it would be difficult but I thought a lot of our boys showed great energy from start to finish, and Andy Robertson was terrific and got his reward with his goal in the final minute.
"It would be disrespectful of me to say that Motherwell were under-strength at the back but it was really nice of Stuart McCall to say it was the best away performance he has seen at Fir Park."
The United boss then explained why he had taken off Ryan Gauld as the youngster looked to grab a hat-trick.
He said: "I was reluctant to take him off but he took a bit of a dunt before his first and was a bit groggy at half-time so we took him off before the end for his own sake - and hopefully he will be okay for the Scotland Under-21s."
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- Paul Paton