The striker - who turned 24 on Sunday - made it 11 goals in his last nine appearances in all competitions with a close-range header in the fourth minute to move the hosts top of the table.
United battled in vain to come back into the game, but Simon Mignolet remained defiant as he kept his third clean sheet of the season.
Brendan Rodgers was forced to change his Liverpool starting XI for the first time in the Premier League this season as a groin injury kept Kolo Toure out. Martin Skrtel replaced the Ivorian at the heart of Liverpool’s defence alongside Daniel Agger.
Wayne Rooney was the notable absentee for the visitors - the striker ruled out with a head injury – with Antonio Valencia dropping to the bench as Ashley Young and Ryan Giggs replaced them.
Steven Gerrard’s corner was met by Agger and as his header flew towards goal, Sturridge reacted quickly to divert the ball into the back of the net from close range.
Rodgers’ side controlled the majority of the half with neat passing and fluid movement, but were unable to test David de Gea in the United goal.
Young – who had been quiet in the first half – went close to equalising for the visitors just after the break with the visitors’ best sight of goal.
Liverpool failed to clear a corner but Young’s half-volley struck Glen Johnson and deflected away.
The rivalry between the two sides began to intensify as the game reached the hour mark, referee Andre Marriner issuing five yellow cards – four of them to United players.
Van Persie fired wide following a Javier Hernandez through-ball and a fine De Gea save also denied Raheem Sterling in stoppage time as Liverpool clung on to record the victory.
Liverpool's victory, however, was tempered by the departure of Johnson late in the game through injury. Watching England manager Roy Hodgson will have been particularly concerned given Phil Jones also limped out in the second half.
