Januzaj’s first start under Moyes began badly when Craig Gardner handed the Black Cats an early lead at the Stadium of Light, capitalising on another mistake by Nemanja Vidic.
Sunderland spurned two good chances to increase their lead before the half, but could not get that all important second goal and United punished them.
Januzaj turned in a Patrice Evra cross to tie things up before completing the turnaround with a great volley that flew into the far corner.
Suarez gave Liverpool the lead in the 13th minute with an improvised finish after playing a great one-two with Jose Enrique.
Daniel Sturridge then doubled the lead just four minutes later thanks to a wonderful solo effort. Captain Steven Gerrard added a third before half-time from the penalty spot to score for the Merseyside outfit for the 15th consecutive season.
Liverpool’s merseyside rivals Everton saw their unbeaten start to the season come to an end as they lost 3-1 to Manchester City.
Romelu Lukaku put Everton ahead in the 16th-minute lead after a brilliant solo run but Álvaro Negredo almost immediately wiped out the advantage, before Sergio Agüero’s excellent tucked finish handed City the half-time lead. Manuel Pellegrini’s men then made sure of victory from the spot, the ball ricocheting in off goalkeeper Tim Howard after Agüero’s penalty had cannoned off the base of the upright.
Elsewhere Newcastle United bounced back from successive Premier League defeats after a Loic Remy double spurred them to a 2-1 victory away to Cardiff while Fulham left it late to inflict a miserable return to Craven Cottage for Mark Hughes as Darren Bent’s goal was enough to see off Stoke City 1-0.