The Reds moved to eighth on the table thanks to a double from Luis Suarez, who also supplied Raheem Sterling with the opener, and the overall performance was applauded by manager Rodgers who has seen his side salute in three of their past four outings.
"You've got to give massive credit to the players," Rodgers told Sky Sports.
"They were magnificent. Looking at the tiredness of some of the teams right now, our intensity and pressure was marvellous.
“We played some terrific football against a Sunderland side under Martin O'Neill that have been very difficult to beat."