The Reds were ahead inside four minutes when birthday boy Sturridge, turning 24 today, diverted Daniel Agger's header into the net following Steven Gerrard's corner.
United came back into the match quickly and a well-worked passing move saw Danny Welbeck test Simon Mignolet for the first time with a low shot.
Minutes later they again had a chance when Ashley Young's low corner somehow evaded all at the front post before also bobbling by Robin van Persie at the back post.
United's resurgent spell fizzled out after 20 minutes and it was Liverpool who next threatened when Glen Johnson was brought down outside the area. Gerrard's curling free kick was saved by David de Gea.
The historically fiery nature of the fixture began to resurface towards the end of the half, with three Manchester United players - Tom Cleverley, Michael Carrick and Van Persie - seeing yellow.
Once the half-time whistle had blown, referee Andre Marriner spoke to both captains - Gerrard and Nemanja Vidic - in an effort to calm things down ahead of the second period.