Everton got their UEFA Champions League qualification hopes back on track with a home win over Aston Villa, but Tottenham Hotspur were held by Hull City.
West Ham United picked up an important home victory over Swansea City, but Fulham tumbled to the foot of the table after being blitzed by Southampton.
Stoke City enjoyed a first league win over Manchester United since Boxing Day 1984 after Charlie Adam's double clinched a 2-1 victory at the Britannia Stadium.
Former United striker Mark Hughes' side took the lead in fortunate fashion on 38 minutes when Adam's long-range free-kick deflected off Michael Carrick and wrong-footed United keeper David de Gea.
Moments later, United lost a second centre-half as Phil Jones joined Jonny Evans in being forced off through injury.
But United responded positively to equalise two minutes after half-time when record signing Juan Mata played in Robin van Persie and the Dutch striker lifted a fine shot beyond Asmir Begovic.
Stoke, though, were back in front five minutes later when Marko Arnautovic failed to connect with Jon Walters' knock-down and the ball was arrowed into the top corner by Adam from 25 yards.
The champions almost snatched a late equaliser, but Begovic produced a wonderful save to tip Wayne Rooney's free-kick against the post.
Sunderland enjoyed a second successive 3-0 win at St James' Park to condemn Newcastle United to a fourth consecutive home defeat.
Gus Poyet's side went ahead with 19 minutes gone when Phil Bardsley went down under Vurnon Anita's clumsy challenge inside the box and Fabio Borini smashed the penalty high into the net.
The lead was doubled just four minutes later when Tim Krul clawed Jack Colback's deflected shot away, but Adam Johnson was on hand to tap home with the keeper berating full-back Davide Santon afterwards.
And Sunderland celebrated a third goal with 10 minutes remaining when Colback exchanged passes with Borini before rifling a shot in to the top corner.
Cardiff climbed off the bottom of the table after a quick-fire double early in the second half secured a vital 2-1 home success over Norwich City, and Solskjaer's first as a manager in the top flight.
Norwich took a fifth-minute lead in south Wales as Martin Olsson found space on the left and his low cross deflected into the path of Robert Snodgrass to score.
New loan signing Wilfried Zaha was brought on as a first-half substitute and set up the equaliser on 49 minutes as he played in Craig Bellamy for a scruffy finish.
Just two minutes later and Cardiff were in front as another new signing - Kenwyne Jones - finished at the second attempt after his initial header had been blocked.
Kevin Mirallas scored a majestic late winner as Everton came from behind to beat Aston Villa 2-1 at home to respond positively to their midweek derby defeat.
Villa have enjoyed a good record at Goodison Park in recent seasons and took the lead on 34 minutes when Leandro Bacuna exchanged passes with Christian Benteke before slipping a shot through Tim Howard's legs.
Everton, who had hit the post after just three minutes through Aiden McGeady, levelled on 74 minutes following a patient build-up which finished with Steven Naismith slotting past Brad Guzan after a clever flick by Steven Pienaar.
With five minutes to go, Everton claimed the points when Belgium international Mirallas curled a stunning 30-yard free-kick over the wall and inside the post.
Shane Long scored his first goal for Hull City, but Steve Bruce's side were pegged back for a 1-1 draw at home with Tottenham.
New signing Long marked his home debut by putting Hull in front on 12 minutes by smartly finishing past Hugo Lloris after fellow January arrival Nikica Jelavic had been involved in the build-up.
Spurs equalised just past the hour mark when Danny Rose's 30-yard shot fell to the feet of Paulinho and the Brazilian rifled his effort past Steve Harper.
Fulham slumped to the bottom of the table after Southampton scored three times in the space of 11 second-half minutes to win 3-0 at Craven Cottage.
Southampton made the breakthrough on 64 minutes after a neat interchange of passes ended with Adam Lallana being played in on the left side of the box and he drilled a low shot past Maarten Stekelenburg.
Another fine passing move brought Southampton's second goal on 70 minutes as Nathaniel Clyne got down the right-hand side before rolling in a low cross which was finished by Rickie Lambert.
England international Lambert then played a precise long pass from inside his own half on 75 minutes which sent Jay Rodriguez down the left and the former Burnley forward cut infield before curling a brilliant shot beyond Stekelenburg.
Kevin Nolan scored a first-half double before Andy Carroll was sent off as West Ham United beat Swansea City 2-0 at Upton Park.
The hosts took the lead after 25 minutes when George McCartney's ball into the box was headed down by Carroll for Nolan, who controlled on his chest before crashing a superb volley into the net.
Their second came in first-half stoppage-time when Stewart Downing's corner towards the back post was headed by Carroll across the face of goal for Nolan to nod home from close range.
However, West Ham were reduced to 10 men in the second half when Carroll was sent off for what referee Howard Webb deemed to be an aggressive elbow to the head of Chico after an aerial tussle.