Manchester United moved level on points with fifth-placed Tottenham after victory at West Ham, who played for 75 minutes with 10 men following the controversial dismissal of Sofiane Feghouli.
Replays showed it was more of a coming together between two players committed to winning the ball than a reckless tackle meant to cause harm.
Antonio Valencia was guilty of an astonishing miss for the visitors before Juan Mata scored from 10 yards after a clever pass by fellow substitute Marcus Rashford.
It was Jose Mourinho’s side’s sixth straight Premier League win and their seventh in all competitions.
Watch Man Utd 2-0 West Ham goal highlights
The Hammers have beaten Bournemouth, Sunderland, Burnley and Hull at home this season, yet their hopes of claiming a first major scalp at London Stadium were undone by the fastest sending off in the Premier League this season.
But Dean, who sent off Southampton’s Nathan Redmond in the 4-1 defeat by Tottenham on Wednesday, brandished a red card for the fifth time this season, much to the fury of West Ham boss Slaven Bilic.
Jones, who was clearly hurt and rolled over several times before receiving treatment, was booed by home fans for the rest of the game each time he touched the ball.
Feghouli is now set to miss his side’s FA Cup third-round home tie against Manchester City on Friday, while Hammers supporters showed their anger at the official by chanting ‘Mike Dean – it’s all about you’.
In the second half, Dean kept his cards in his pocket after Cheikhou Kouyate’s reckless challenge on Henrikh Mkhitaryan.
This was far from vintage Manchester United, yet Mourinho’s team started 2017 as they finished 2016 – with three points.
They are now unbeaten in their past 13 games in all competitions, while they have taken 25 points from the last 33 on offer.
Valencia will surely be haunted by his 36th-minute miss. It was a brilliant save by Darren Randolph to deny him from close range, but the Ecuador international should have buried the chance, as should Jesse Lingard, who hit the post with the follow-up.
Mourinho’s decisions to bring on Mata at the start of the second half and Rashford before the hour mark proved decisive.
David de Gea twice saved well from Manuel Lanzini, before Michail Antonio’s glancing header flashed agonisingly wide as the Hammers threatened.
And shortly before Mata broke the deadlock, Antonio found himself clean through after Lanzini’s perfectly weighted pass, only for De Gea to block his effort.
Man of the match, Marcus Rashford (right) was excellent after coming on as a substitute. The teenager provided his side with a major boost and was a constant threat, setting up one goal and hitting a post
“Ten men against a team like this is very hard – but we had chances.
“I am disappointed with the result and frustrated by how we lost it, but I am proud of my players.”
Manchester United manager Mourinho: “It was hard for us to think well with one more man – and it was very hard for them physically.
“I was happy with my choices in Juan Mata and Marcus Rashford, they gave us what we needed. Rashford is very professional and very mature. He is a Manchester United player with Manchester United DNA.
“I don’t feel sorry for West Ham – I didn’t watch the decisions. I think if you talk about decisions, we are the champions of bad decisions.”
Manchester United are now 13 games unbeaten in all competitions – longest run since March 2013. West Ham have lost consecutive Premier League games without scoring for the first time under Bilic.
West Ham are back in action on Friday when they host fellow Premier League side Manchester City in the FA Cup third round (19:55 GMT kick-off).
Manchester United start their defence of the famous trophy at home against Championship club Reading – managed by former Old Trafford defender Jaap Stam – on Saturday (12:30).