Huddersfield Town's 4-1 home victory over Bournemouth earlier in the day meant Newcastle started their home clash against United in the Premier League's bottom three.
Yet they responded with a gritty display, riding their luck at times to take the points courtesy of Matt Ritchie's 65th-minute winner which propelled them from 18th to 13th.
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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.
Tottenham Hotspur's 1-0 victory over Arsenal on Saturday had lifted the north London club to within four points of United and Liverpool sliced the gap to two after Roberto Firmino and Mohamed Salah scored in a nonchalant 2-0 win at Southampton in Sunday's late kickoff.
Fifth-placed Chelsea can move to within three points of United with victory at West Brom on Monday. There was a warm handshake between Benitez and Mourinho when the final whistle sounded at a tumultuous St James' Park to confirm Newcastle's first home league win since October.
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But their previous history has been marked by frostiness — a result of former Liverpool manager Benitez twice getting the better of Mourinho's Chelsea in Champions League semi-finals.
The fact that they have both managed Chelsea, Real Madrid and Inter Milan, with Mourinho enjoying a superior record, meant Benitez's triumph on Sunday, only his second in the Premier League against Mourinho, had added meaning. Ritchie rifled a shot past David De Gea in the 65th minute to punish a profligate United side who wasted several good chances with Anthony Martial and Alexis Sanchez culpable.
Newcastle dug deep for their manager and debutant keeper Martin Dubravka made several superb saves.
"They fought like animals," Mourinho said of Benitez's side. "Newcastle's players gave the sacrifices all managers like to see. Were they lucky? Yes. But sometimes you deserve that luck. They fought for their lives and that's a beautiful thing."
Martial was denied by a great save from Dubravka and had two efforts cleared off the line after the break.
Sanchez inexplicably failed to fire into an empty net after rounding Dubravka, shortly before Ritchie struck the winner.
"We had games in the past when we conceded late. We got lucky with some shots, but we showed the character, the commitment and the desire today," said Benitez said.
Liverpool were too slick for a feeble Southampton as they condemned the south coast side to a place in the bottom three.
Salah punished a mistake and squared for Firmino to score in the seventh minute and the livewire Egyptian then stroked home the second before halftime after a snappy passing move. United have 56 points, Liverpool 54 and Tottenham 52 with Chelsea on 50.
It is equally tight at the bottom where the so-called trap door is looking more like a revolving door. Huddersfield escaped the bottom three on Sunday as they snapped a five-game losing sequence.
Alex Pritchard fired Huddersfield in front after seven minutes and although Junior Stanislas levelled, the hosts were ahead again before the break thanks to Steve Mounie's 27th-minute header from Aaron Mooy's delivery.
Beninese striker Mounie's shot was deflected in by Steve Cook after 66 minutes and Rajiv van la Parra tucked away a stoppage time penalty to complete a satisfying afternoon for David Wagner's side.
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