Mourinho has never won on Tyneside in the Premier League and that run extended to seven matches after Matt Ritchie stunned the visitors with a 65th-minute victor.
The result also left second-placed United a whopping 16 points behind leaders Manchester City and looking anxiously over their shoulders in what looks like becoming a tense battle for the remaining Champions League places.
They are just one point above the bottom three and have kept just two clean sheets in the last 17 matches.
Newcastle dug deep for their manager and debutant keeper Martin Dubravka made several superb saves.
However, Ritchie's 65th-minute victor came against the run of play and the Magpies had to defend for their lives as time ran down.
Adding to Mourinho's frustration, the goal stemmed from a free-kick awarded for a needless dive by United defender Chris Smalling. In the second half, we had Alexis [Sanchez] with an open goal and then we had an accumulation of situations where it's incredible that we didn't score.
One exception was Alexis Sanchez and he nearly put them ahead in the 57th minute when he rounded Dubravka before his goal-bound shot was blocked by Florian Lejeune.
It looked a clear penalty, but referee Craig Pawson waved the appeals away.
A few moments later and Sanchez saw his shot deflected wide after a powerful run into the Newcastle box, before the Chilean got on the end of a pass from Lukaku and took it round the goalkeeper, only for Lejuene to come flying in with the block.
Manchester United will meet with Huddersfield Town again next weekend in the fifth round of the FA Cup, with the former Real Madrid manager hoping for a more subtle approach from the Terriers towards Alexis Sanchez, after he became the most fouled player in the Premier League last weekend.
On the other hand, Newcastle could have Joselu back in the starting XI after he missed last week's trip to Crystal Palace due to illness.
Elsewhere at the John Smith's Stadium, Huddersfield climbed out of the relegation zone after a 4-1 win against Bournemouth.
He admits that a defensive mistake led to Newcastle taking the lead and feels with luck in the Magpies' corner, it was never going to happen for his players today.