Spanish striker Fernando Torres held off Rio Ferdinand to lash Liverpool in front after 65 minutes and David Ngog added a second goal in stoppage time to spark celebrations at Anfield after four morale-sapping defeats on the spin.
The deserved victory revived Liverpool's hopes of a title challenge, taking them to fifth place on 18 points from 10 games, four behind United and six adrift of leaders Chelsea who went top on Saturday with a 5-0 thrashing of Blackburn Rovers.
Arsenal edged above Tottenham Hotspur ahead of next week's north London derby into third place on goal difference although their defensive fragility returned to haunt them as they let a two-goal lead slip at West Ham United to draw 2-2.
Robin van Persie and William Gallas had put the Gunners ahead by half-time but West Ham replied through Carlton Cole and Alessandro Diamanti's penalty at Upton Park.
Manchester City's hopes of moving into the top four were frustrated when they also surrendered a two-goal lead in a 2-2 home draw against Fulham.
BETTER TEAM
Everton lost 3-2 at Bolton Wanderers, another source of pleasure for Liverpool's supporters whose mood would have been further enhanced by United manager Alex Ferguson's later admission that his side had been second best.
"It was a disappointing performance in the first half. We didn't handle the atmosphere or the decision against us," Ferguson told Sky Sports.
"Liverpool were the better team and created the better chances. They... deserved their victory."
A typically rumbustious match ended with only 20 players on the pitch after United's Serbia central defender Nemanja Vidic and Liverpool's Argentina midfielder Javier Mascherano were shown red cards in the frenetic closing stages.
Vidic, who was dismissed for hauling down Dirk Kuyt on the halfway line, was also sent off in both United's league defeats by Liverpool last season.
"It was a massive win for us," Torres told Sky Sports. "We needed to win to stay in the title race," added the Spain striker who played with a pain-killing injection in a groin injury and was substituted after his goal.
Liverpool manager Rafa Benitez came under mounting criticism after league losses to Chelsea and Sunderland sandwiched between Champions League defeats by Fiorentina and Olympique Lyon.
However, he could smile on Sunday after his team produced a display full of vim and vigour despite missing injured captain Steven Gerrard.
"It was about mentality, about everybody working together from the goalkeeper to the last fan in the Kop," Benitez, who gambled by starting an "80 percent" fit Torres, told Sky Sports.
BEACH BALLS
United supporters predictably released several beach balls before kick-off, a reminder of the freak goal that beat Liverpool at Sunderland last week, but they had little else to laugh about as their side were outplayed.
Liverpool dominated the first half with
