It means Brendan Rodgers' men have continued their impressive start to the new season, making it three wins out of three for only the third time in the Premier League era.
The visitors had their chances with Robin van Persie flashing an overhead kick wide just moments after the hosts' opener.
And the Dutchman missed a great opportunity three minutes from time when he crashed a shot past the near post to ensure David Moyes' winless run at Anfield stretched to 13 games.
It capped a great afternoon for the Merseysiders who marked the upcoming 100th anniversary of Bill Shankly's birth with a significant triumph over the champions.
4’ GOAL – Liverpool 1-0 Man United: Gerrard's right-wing corner is flicked on by Agger for Sturridge to nod home from close range. What a start at Anfield!
6' CHANCE FOR UNITED: The visitors almost level immediately. A right-wing free-kick is headed back across goal towards Van Persie, who flashes an overhead volley over the bar.
45' FISTICUFFS: A United attack ends with Young sending a devilish cross in towards Van Persie, who claims Skrtel knocked him on the head with his elbow. A coming together ensues with Gerrard involved in a heated debate with the United striker. Referee Andre Marriner takes the two captain's to one side in order to defuse the situation.
52' CLOSE: Agger fails to get any length on his headed clearance, allowing Young the chance to crash in a goal-bound volley that is superbly blocked by Johnson.
77' GREAT SAVE: Mignolet dives to his left to beat away a thumping drive from Nani after a fine run from the right by the United winger.
87' CHANCE FOR UNITED: Hernandez plays Van Persie in on the right side of the area but the Holland striker fizzes wide at the near post. Big miss for Moyes and co.
Sturridge becomes only the second Reds player to score in each of the opening three Premier League games of a season. The last man to achieve the feat was Robbie Fowler in 1994-95.
This was David Moyes’ 13th visit to Anfield as a manager. He has drawn 7 and lost 6 of those encounters.
That was only Liverpool's second clean sheet in the last 15 league clashes with Manchester United.
It was Man United's first defeat in 14 matches on their travels.
TALKING POINT - How far can Liverpool go this season? Despite missing the suspended Luis Suarez, Brendan Rodgers' side top the Premier League after three matches with a trio of 1-0 victories. With no European football to contend with they can focus all of their attention on their Champions League push and must be doing their chances the world of good with this fine start to the campaign. The Reds are also expected to add to their squad in the next 24 hours.
MAN OF THE MATCH - Martin Skrtel (Liverpool): The Slovakian defender came back into the side for the first time this season and was a rock at the back as Liverpool held firm under incessant pressure in the second half.
PLAYER RATINGS -
LIVERPOOL: Mignolet 7, Johnson 7, Enrique 6, Agger 6, Skrtel 8, Lucas 6, Henderson 6, Gerrard 7, Coutinho 6, Aspas 6, Sturridge 7. Subs: Sterling 6, Wisdom 6, Alberto 6.
MANCHESTER UNITED: De Gea 6, Jones 5, Vidic 7, Ferdinand 6, Evra 6, Cleverley 6, Carrick 5, Young 6, Welbeck 6, Giggs 6, Van Persie 6. Subs: Valencia 6, Nani 6, Hernandez 7.
MATCH IN A TWEET