Yohan Cabaye's 61st-minute goal earned Newcastle its first win at Old Trafford in 41 years and left United supporters further disheartened after a loss by the same scoreline to Everton on Wednesday.
The way the champions are playing, a place in next season's Champions League could even be out of reach, although the top four is wide open with the big teams continuing to drop points.
Also Saturday, Sunderland stayed bottom after squandering a lead to lose 2-1 at home to sixth-place Tottenham, which has picked up seven points from a possible nine since being humiliated 6-0 by Man City last month. Crystal Palace beat Cardiff 2-0 for a third win in four matches since the departure of Ian Holloway and Norwich won 2-0 at West Bromwich Albion.
There was a minute's applause before each Premier League game in honor of former South Africa president Nelson Mandela, who died on Thursday at the age of 95.
Chelsea and Man City were looking to apply pressure on Arsenal but couldn't hold onto their leads away from home.
Andre Schuerrle put Chelsea in front and then equalized for 2-2 after Stoke had hit back through goals by Peter Crouch and Stephen Ireland, only for Assaidi to grab the winner with seconds left of normal time.
"I don't feel comfortable enough to tell you what I think about the game. We're in trouble,'' said Mourinho, bemoaning his team's lack of organization.
Sergio Aguero moved to 12 goals for the campaign two behind Suarez's league-high tally to give City the lead at Southampton, but Pablo Osvaldo delivered a brilliant equalizer just before halftime by leaving Vincent Kompany on the ground, turning Pablo Zabaleta and floating in a curling shot from the angle just inside the area.
"I'm pleased with the point,'' said City manager Manuel Pellegrini, whose side's away form has been erratic this season.
Suarez couldn't reproduce his exploits of Wednesday, when he scored four stunning goals against Norwich, but he once again proved to be the difference for Liverpool in a game of three own goals against West Ham.
Guy Demel and Joey O'Brien put in their own net to bookend the victory after good work by Suarez, who scored himself with a powerful header in the 81st minute to make it 3-1.
Mamadou Sakho netted Liverpool's second, with West Ham replying through Martin Skrtel's own goal before losing Kevin Nolan to a red card with eight minutes left.
"In the end we had 29 attempts at goal, and we could have scored more than four. It was a great victory,'' said Liverpool manager Brendan Rodgers, whose captain Steven Gerrard limped off injured midway through the second half.
Liverpool has scored 17 times in its last four home games but United found goals hard to come by this week, failing to score in successive games to lose back-to-back home matches in the league for the first time in 11 years.
Without the suspended Wayne Rooney and with Robin van Persie lacking sharpness in his first match back after a month out, United lacked a cutting edge against Newcastle, which controlled midfield and pounced when Cabaye's sidefooted effort deflected into the corner.
"When I came here I knew it wasn't always going to be easy and it's proving that way,'' Moyes said.
As the pressure on one coach increases, so it relents on another as Tottenham manager Andre Villas-Boas punched the air in delight after his team's second away win in four days. John O'Shea's own goal in the 50th sealed Spurs' victory at the Stadium of Light.
-AP