Brendan Rodgers' side came into the clash at Anfield buoyed by back-to-back victories over Stoke City and Leicester City but they fell short of making it three consecutive league wins for the first time this season.
Captain Steven Gerrard, so impressive at Leicester on Tuesday, was back on the Liverpool bench and replaced by Philippe Coutinho.
Gus Poyet's side remained solid throughout, with the likes of Coutinho, Adam Lallana and Raheem Sterling unable to provide frontman Rickie Lambert with any clear chances to break the stalemate.
Gerrard was introduced in place of Lallana midway through the second half, but Liverpool's talisman was unable to inspire his side to find a winner as they were forced to settle for a share of the spoils.
Goalmouth action was scarce, but Sunderland had the best chance before the break when Brown powered a header over the crossbar from Seb Larsson's corner on the stroke of half-time.
Liverpool appealed for a penalty in the 51st minute when Moreno's low cross deflected off John O'Shea and struck Jordi Gomez on the arm, but once again referee Neil Swarbrick was unmoved.
Wickham then flashed a left-footed volley across goal as Sunderland threatened an opener, before Liverpool's first effort of note arrived in the 64th minute as Lucas Leiva's strike from distance brought a comfortable save out of Costel Pantilimon.
The Romanian goalkeeper was in action again 12 minutes from time, parrying Coutinho's drive following a mazy dribble and pass from Sterling.
Gomez stung the palms of Simon Mignolet with a rasping drive three minutes later and although Liverpool enjoyed the majority of possession in the closing stages, Rodgers' men failed to make the crucial breakthrough.
