Adam Lallana and George Johnston were both dismissed as Spurs closed the gap on the teams above them.
A strong Liverpool team, which also included Danny Ings, Dominic Solanke and Ben Woodburn, were unable to cancel out Roles' 55th-minute strike.
Lallana was sent off for his reaction to George Marsh's challenge and Johnston collected a second yellow card late on.
Spurs are a point behind Sunderland with a match in hand, while Liverpool are only one point ahead of Arsenal.
Spurs: 12 Feb v West Ham (A) PL2
Liverpool: 13 Feb v Bristol City (A) PL Cup