Danny Rose's second-half strike gave Tottenham a point after Liverpool looked on course for a second successive away win in north London.
Liverpool beat Arsenal 4-3 at Emirates Stadium on the opening weekend of the Premier League season and were in control through James Milner's penalty, scored just before the break after Erik Lamela fouled Roberto Firmino.
Tottenham goalkeeper Michel Vorm had earlier saved brilliantly from Coutinho, and Joel Matip had glanced a header off the bar, as Liverpool tried to make the most of their superiority.
Liverpool also had a goal ruled out after a controversial offside decision against Sadio Mane.
Arsenal beat Watford to earn their first victory of the season. Both sides had one defeat and a draw from the opening two league matches but Arsenal's impressive first-half performance earned them three points.
A Santi Cazorla penalty, Alexis Sanchez's fumbled effort and Mesut Ozil's header gave the Gunners a 3-0 lead at half-time. Substitute Roberto Pereyra scored for the Hornets on his debut but it proved to be a consolation for the hosts.
Walter Mazzarri's side put in a much-improved performance after the break but the Italian was made to wait for his first win as Watford manager.
Substitute Marcus Rashford scored an injury-time winner as Manchester United finally overhauled a stubborn Hull at a wet KCOM Stadium.
The 18-year-old - making his first appearance of the season - steered home Wayne Rooney's cross to spark wild celebrations on the away bench.
Moments earlier, David Meyler had blazed over in a rare Hull attack. But it was a deserved win for United, who had gone close though Rooney, Zlatan Ibrahimovic and Paul Pogba.
United and Chelsea are now the only Premier League sides with a 100% record from three games, with Manchester City - who have two wins from two games - playing West Ham tonight.
Tottenham (Rose 72') 1 Liverpool 1 (Milner 43')
Chelsea (Hazard 9', Willian 41' & Moses 89') 3 Burnley 0
Crystal Palace (Dann 93') 1 Bournemouth 1 (King 11')
Everton (Given - OG 51') 1 Stoke City 0
Leicester City (Vardy 32' & Morgan 52') 2 Swansea City (Fer 80')
Southampton (Rodriguez 85') 1 Sunderland 1 (Defoe 80')
Watford (Pereyra 57') 1 Arsenal 3 (Cazorla 9', Sanchez 40' & Ozil 46')
Hull City 0 Manchester United 1 (Rashford 92')
West Bromwich Albion vs Middlesborough - 10:30pm AEST
Manchester City vs West Ham United - 1:00am AEST