Quickfire goals from Diogo Jota and Darwin Nunez before the break and Mohamed Salah's second-half effort helped Jurgen Klopp's side maintain their 100 per cent home record in the Premier League this season.
The Reds showed their support to Luis Diaz during the game. Jota held aloft Diaz's number seven shirt after scoring, with the Colombian not featuring in Liverpool's squad following reports his parents had been kidnapped in his homeland.
Liverpool's latest victory - their eighth in a row in all competitions at Anfield - was their seventh from 10 league games this campaign and lifted them back to within three points of leaders Tottenham.
Forest rarely threatened and, although they hit the woodwork through Anthony Elanga's late volley, they were forced to defend in numbers as their winless league run was stretched to six matches.