Crystal Palace's win at Stamford Bridge last week closed the gap between Spurs and Chelsea to seven points, which has now been reduced to four after victory in the early kick-off.
Antonio Conte's men will have the chance to extend the gap against Bournemouth in Saturday's late kick-off, but have Tottenham breathing down their necks.
Trippier, who was named man of the match as he stood in for Kyle Walker, told Sky Sports 1: "We believe in ourselves and as a team.
"We just have to keep performing like today. We want to take it game by game, we can't affect Chelsea but we have to focus ourselves, take it game by game and see where it takes us."
Dele Alli opened the scoring with a curling effort from the edge of the area, before Eric Dier and a double from Son Heung-min sealed a comprehensive win.
More to follow.
Additional reporting by the Press Association.