The Egypt international rounded off the win, which was the Merseyside club's eighth in a row in all competitions at Anfield and maintained its 100% start at home in the league.
Liverpool's players also showed their support for teammate Luis Diaz, who was absent from the squad after his parents were kidnapped in Colombia on Saturday. Diaz’s mother was later rescued and his father remained missing, authorities said.
Diogo Jota opened the scoring for the home team in the 31st minute and held up Diaz's No. 7 jersey after his goal.
Darwin Nunez doubled Liverpool's lead four minutes later before Salah's strike in the 77th.
Liverpool’s latest victory was its seventh from 10 league games this campaign and lifted the team back to within three points of leaders Tottenham.
Forest rarely threatened and, although Anthony Elanga’s late volley hit the woodwork, the visitors were forced to defend in numbers.
Forest's winless run now stretches to six matches.
AP soccer: https://apnews.com/hub/soccer