Premier League leaders United dominated their old rivals for much of the Old Trafford clash with Robin van Persie and Nemanja Vidic, albeit just offside when he deflected in Patrice Evra's header, giving them a 2-0 lead.
Ex-Chelsea forward Sturridge, introduced at half-time despite having scored on his club debut in the FA Cup win over Mansfield Town last weekend, was straight into the action and pulled a goal back on 57 minutes after Steven Gerrard's shot was saved.
Looking twice as lively as any other visiting player, Sturridge then had three decent chances to level as United panicked at the back before holding on in a game where they should have been home and dry.
Although his finishing was not up to scratch, Liverpool fans will be pleased to see a player with attacking intent in the box after spending the first half of the season almost entirely dependent on 15-goal Luis Suarez - who was disappointing on the day.
"He (Sturridge) was terrific when he came on and we were much better in the second half," Liverpool manager Brendan Rodgers told Sky without revealing why the England man had not started having been starved of football latterly at Chelsea.
"In the second half, after we conceded the goal, we could have given up the fight but that is the nature of the group. In the end, I thought we maybe deserved something from the game. The goals we conceded were disappointing.
"We will learn from days like today, even though we didn't get the result."
Rodgers, whose side are down in eighth in his first season in charge, may well learn that even at mighty United it is worth having a tenacious striker who is keen to impress in your ranks but he at least deserves credit for the quick substitution.
Despite the late nerves, United boss Alex Ferguson was pleased with the display.
"It obviously doesn't matter when you play Liverpool, it is a big game and I hope it's an important result," he said.
"We were fantastic until their goal, which inspired them. They made a fist of it in the last half hour and it made it an engrossing game.
"We played well. It was as good a performance as we've produced for a while. When you play Liverpool you have to be at your best form to win and we were."