A first-half own goal from Wes Brown and a Ryan Babel winner close to the end were enough for Rafa Benitez to take three points off rival Sir Alex Ferguson for the first time.
The cautious Liverpool boss started with his two most influential players, Fernando Torres and captain Steven Gerrard, on the bench but new £5.5million signing Albert Riera made his first start for the Reds.
The decision looked to have been flawed as the visiting side launched an attack straight from the kick-off. New £32million striker Dimitar Berbatov blasted the ball against the hand of Martin Skrtel in the box, only for referee Howard Webb to wave away the penalty appeals.
United, who were attacking the Kop end, piled on the pressure in the opening stages and it took them only two-and-a-half minutes to take the lead thanks to
Carlos Tevez's right-foot strike.
An accurate crossfield ball from Anderson found Berbatov on the edge of the box and the Bulgarian easily held off Liverpool's stand-in captain Jamie Carragher's challenge.
The striker made room for himself and cut the ball back across the area to an on-rushing Tevez who side-footed the ball over Skrtel and past a stranded Pepe Reina in goal.
Dirk Kuyt's 25-yard volley on five minutes had the crowd on their feet as it flew past the post and the Dutch winger had a great chance to equalise two minutes later when a looping corner by Alvaro Arbeloa almost crept under the bar.
Edwin van der Sar managed to palm the ball out but it fell at Kuyt's feet and the number 18's effort was superbly saved by the arm of the outstretched United shot-stopper.
Having been pinned in their own half for most of the opening 20 minutes, the home side had to rely on a stroke of luck to equalise on 27 minutes.
A hopeful long-range effort from Xabi Alonso took a wicked deflection off Patrice Evra that sent the ball bouncing across the front of the goal.
Feeling he had to deal with the danger, van der Sar came flying off his line and, in an attempt to push the ball to safety, he played it straight onto the knee of a back-tracking Brown who watched it roll into his own net.
Anderson had a good opportunity to restore United's one-goal lead a minute later, but he couldn't keep the ball down after it was rolled towards him at the near post by Tevez.
Liverpool started to get back into the game but, with no support for Robbie Keane, the United defence had no trouble dealing with any crosses and the visitors always looked dangerous on the break with Wayne Rooney on the right wing often running at Arbeloa.
The home side came out for the second half looking much brighter and, two minutes after the restart, a low driven ball by Alonso eluded the United defence until Evra managed to stretch out his left leg to and scoop the ball off the toe of Kuyt who was lurking at the back post.
Either side could have taken the lead with speculative efforts from Keane and Berbatov but a 30-yard volley in the 65th minute from substitute Ryan Giggs saw Reina pull off the save of the game by tipping the ball over his bar.
Outplaying their rivals in the second 45, Liverpool took the lead after man-of-the-match Javier Mascherano fought his way to the byline and cleverly knocked the ball through the legs of Giggs.
Kuyt took over from the Argentinian and threaded the ball to an unmarked Babel who hammered home from eight yards to secure the three points.
Rooney could have pinched a point in the last minute of stoppage time with a thunderous 20-yard drive but he failed to cap his impressive performance with a goal as the ball flew wide of a thankful Reina.