Arsenal, meanwhile, conceded two first-half goals as they lost to Watford at the Emirates
Georginio Wijnaldum earned Liverpool a hard-fought point as they drew 1-1 with Premier League leaders Chelsea at Anfield.
Antonio Conte's side went into the night eight points clear of Arsenal and held a 10-point lead over a Liverpool side for struggling for any remnants of form.
Klopp's side controlled much of the possession in the opening half, but came undone when Chelsea were awarded a freekick on the edge of the area.
A three-man wall was established, but while Mignolet was still organizing his defence, David Luiz unleashed a venomous shot which cannoned in off the post.
Roberto Firmino missed a wonderful chance to level the game after the break after a flowing Liverpool move. He found himself on the penalty spot and Thibaut Courtois was beaten all ends up, but his shot flew over the bar.
The equaliser came as Jordan Henderson floated a wonderful cross-field ball to James Milner at the back post. Milner headed across goal and the Dutch midfielder was able to finish past Courtois.
Arsenal missed the chance to keep pace with their London rivals as they slipped to a 2-1 defeat at home to Watford.
Former Tottenham player Younes Kaboul opened the scoring with a freekick on 11 minutes - his effort was helped in by an Aaron Ramsey deflection.
Only three minutes later, Troy Deeney doubled the away side's advantage with a rebound inside the Arsenal area. Alex Iwobi threw Arsenal a lifeline with his second half strike, but it wasn't enough to stir a comeback reminiscent of their trip to Bournemouth earlier this season.
Speaking of Bournemouth, they were beaten 2-0 at home to Crystal Palace as Sam Allardyce's side enjoyed their first away clean sheet since St Stephen's Day in 2015.
Palace took the lead through Scott Dann just after the break and Belgian Christian Benteke scored his ninth league goal of the season in stoppage time.
At times, Palace essentially have a back-seven. Allardyce seems content to allow his front-three to work in isolation.— Seb Stafford-Bloor (@SebSB) January 31, 2017
Shane Long's second half goal wasn't enough to earn Southampton a point away to Swansea this evening. Alfie Mawson had put the home side ahead before the break, before Long notched his second goal for the club in three games.
Gylfi Sigurdsson scored on 70 minutes to make it 2-1 and to ensure Swansea picked up their first home league win under Paul Clement.
While the biggest part of Burnely's night was arguably the signature of Robbie Brady from Championship side Norwich, Sean Dyche's side had Sam Vokes to thank after his late goal secured them a 1-0 win over champions Leicester City at Turf Moor.
Elsewhere tonight, Sunderland held Tottenham to a scoreless draw at the Stadium of Light.