With second-placed Arsenal not playing Southampton until Monday, United took full advantage through an own goal by Danny Mills and a battling display after midfielder Darren Fletcher was dismissed for a second bookable offence in the 65th minute.
United moved up to 46 points with their 15th victory in 19 games, followed on 42 by both Arsenal and Chelsea, who recovered from Friday's mauling by Charlton Athletic with an emphatic 3-0 win over Portsmouth.
Charlton took fourth spot following a 1-0 victory at Tottenham Hotspur, who dropped into the relegation zone, and Fulham slipped to fifth after a 3-0 defeat at Aston Villa. Teenager Wayne Rooney came off the bench to clinch Everton's 1-0 victory over Birmingham City, and Newcastle United fell to seventh after losing 1-0 at home to Blackburn Rovers.
Manchester United, who absorbed intense pressure in the closing minutes, went ahead after 14 minutes when a shot from South African Quinton Fortune took a wicked deflection off Mills and left Boro keeper Mark Schwarzer stranded.
Boro enjoyed plenty of second-half possession but failed to create any clearcut opportunities, and only a fantastic reflex block by Schwarzer and the crossbar denied the champions a second through Paul Scholes.
United manager Alex Ferguson felt his side were deserved winners.
"I don't think they (Middlesbrough) made a chance in the whole match," he told Sky Sports. "I don't think (goalkeeper) Tim Howard made a save."
Ferguson was also unimpressed by Fletcher's red card.
"The referee's made a rod for his own back really -- the first booking was ridiculous," Ferguson said. "If you go on that principle, there should have been four or five sent off."
CHELSEA BATTLE
Chelsea, whose 4-2 defeat by Charlton was their second loss in three league games, were frustrated at Stamford Bridge until second-half strikes by defender Wayne Bridge and midfielders Frank Lampard and Geremi.
Bridge broke the deadlock with a solo effort in the 65th minute, Lampard found the net following Adrian Mutu's pass and Geremi superbly volleyed his first goal for the club eight minutes from time.
"I was waiting for this performance," Chelsea coach Claudio Ranieri told reporters. "We knew December was a bad month for us and I'm sure in the new year it will be better."
Liverpool were haunted by their former players in a 2-2 draw at Manchester City.
Robbie Fowler was the toast of the home fans after earning a 30th-minute penalty, converted by another former Liverpool striker Nicolas Anelka, and denying his old club victory with an injury-time equaliser.
Gerard Houllier's side had come from a goal down to take the lead through midfielders Vladimir Smicer and Dietmar Hamann.
Bottom club Wolverhampton Wanderers beat fellow strugglers Leeds United 3-1 to cut the gap at the foot of the standings to three points. Leeds have 17 points, one less than Spurs, who suffered their fifth consecutive defeat in all competitions, and Leicester City, who drew 2-2 at Bolton Wanderers.
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