Moyes was without Wayne Rooney due to a head injury that looks set to rule him out of England´s forthcoming World Cup qualifiers and in his absence, the Scot´s poor record at Liverpool continued.
Sturridge, who could benefit from Rooney´s absence for England against Moldova and Ukraine, scored the only goal in the fourth minute, having also been the match-winner in the 1-0 wins over Stoke City and Aston Villa.[break]
His early header means Liverpool are the only team to have won their opening three fixtures, although Tottenham Hotspur could match them if they prevail at north London derby rivals Arsenal later on Sunday.
Although the season remains young, it was a painful defeat for United, who already trail their old rivals by five points.
The game was preceded by a minute´s applause for the late Bill Shankly, who would have turned 100 on Monday, and the legendary former Liverpool manager would have appreciated his side´s purposeful start.
There were less than four minutes on the clock when Liverpool struck, with Sturridge stepping off the line to glance Daniel Agger´s header past David de Gea and claim his 11th goal in his last nine games.
Initially, United struggled to react, and Robin van Persie´s frustration told late in the half when he was booked for flying in on Daniel Agger before angrily clashing with Martin Skrtel.
United also lost Phil Jones to an apparent ankle injury before half-time, but there was a renewed determination to their play in the second period.
Ashley Young had a volley blocked by Glen Johnson and Liverpool goalkeeper Simon Mignolet had to field a Ryan Giggs header before parrying a rasping shot from substitute Nani.
Johnson hobbled off for Liverpool after hurting himself in a block tackle but the hosts survived, with Van Persie spurning a good late chance by slashing wide of the near post in the 87th minute.
In the day´s other lunchtime game, Swansea City recorded their first victory of the season with a 2-0 success at West Bromwich Albion.
The home side recalled Nicolas Anelka after he was granted compassionate leave due to the death of a close friend, but they lost to a 22nd-minute Ben Davies volley and a late Pablo Hernandez strike.
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