The Brazillian clutched his ankle after a challenge from Didier Ndong late in a first half where Liverpool failed to turn 80% possession into clear chances.
Sunderland threatened briefly in each period, with Steven Pienaar and Duncan Watmore taking heavy touches when presented with openings.
But as Jurgen Klopp’s side continued to press, it was Coutinho’s replacement, Divock Origi, who found the net with what appeared to be a right-foot cross from the left side of the area.
It sparked relief at Anfield and when Ndong felled Sadio Mane in the box, James Milner converted a spot-kick to make it 14 games unbeaten in all competitions for the Reds.
Chelsea will move back to the top of the table should they beat Tottenham in Saturday’s late kick-off but Liverpool have clear momentum and last tasted defeat in the Premier League in August.