Man Utd dominate Man City in dream start for Carrick
The Red Devils dominated at Old Trafford and were only made to wait until the final 25 minutes to seal victory by the inspired Gianluigi Donnarumma and because they had three goals ruled out for offside.
Bryan Mbeumo marked his return from the African Cup of Nations (AFCON) by firing home the opening goal before Patrick Dorgu sealed just a second win in eight games for United.
Victory lifts Carrick's men into the top four, but their win will be celebrated just as much in north London as Arsenal close in on a first league title in 22 years.
Mikel Arteta's men can open up a nine-point lead at the top when they visit Nottingham Forest later on Saturday.
Carrick's bold team selection paid off as both the in-form Benjamin Sesko and Matheus Cunha made way for the return of Mbeumo and Amad Diallo from their international duties at AFCON.
Harry Maguire also returned for his first start in two months and should have scored inside the first two minutes.
The centre-back rose highest to meet Bruno Fernandes' corner but crashed his header off the crossbar from point-blank range.
City are set to seal a deal for Crystal Palace captain Marc Guehi, but ravaged by injuries in defence, Pep Guardiola named inexperienced duo Max Alleyne and Abdukodir Khusanov at centre-back.
City's makeshift back line struggled to keep United at bay all afternoon and would have been embarrassed but for the brilliance of Donnarumma in goal.
The Italian's first major intervention came midway through the first half to parry Dorgu's effort.
Donnarumma was twice beaten before the break but both Diallo and Fernandes strayed offside before rounding the goalkeeper to score.
Guardiola tried to awaken the visitors with a double substitution at half-time, introducing Nico O'Riley and Raya Cherki.
But City's title challenge has faded fast in a four-game winless run in the Premier League since the turn of the year.
Donnarumma continued to defy the home side until beyond the hour with a stunning double save from Diallo's powerful strike and Casemiro's follow-up effort.
City played a big part in their own downfall when the opening goal finally arrived 25 minutes from time.
Cherki's poor free-kick allowed United to sprint forward in numbers and Fernandes' pass was perfectly weighted for Mbeumo to fire low and hard beyond Donnarumma's long levers.
Cunha came off the bench to make the second as Dorgu caught Rico Lewis sleeping to steal in at the back post.
Guardiola appeared to waive the white flag as he replaced Erling Haaland 10 minutes from time to reserve the Norwegian's energy with City still fighting in four competitions.
Diallo nearly sealed a stunning individual display when he hit the post in the 90th minute.
Mason Mount then rolled in Cunha's cross with his first touch after replacing Fernandes only for VAR to come to the visitors' rescue again for offside.
But the damage had already been done to City's title aspirations, making victory all the sweeter for Carrick on his return to the Theatre of Dreams.