Thanks to their superior goal difference, Spurs will only need a point at already-relegated bottom side Norwich City on Sunday to qualify for Europe's elite competition.
In the end, a draw was a disappointing outcome for both clubs in their respective ambitions, Liverpool's to reclaim the title and Tottenham's to finish in the top four.
Mohamed Salah and Luis Diaz allowed Juergen Klopp's Liverpool to close the gap to six points at the top, and they also have a game in hand over City.
Chelsea will face London rivals Tottenham Hotspur in the semifinals.
A mistake by Liverpool keeper Alisson gifted Tottenham's Son Heung-min a 74th-minute equaliser the hosts fully deserved although the visitors were fuming about some contentious decisions.
Spurs beat Norwich City 3-0 at home, while Ralf Rangnick made a winning start as Manchester United's interim manager with a 1-0 victory over Crystal Palace.
Former Chelsea and Inter Milan boss Conte replaces Nuno, who was fired on Monday after 17 matches in charge, with Saturday's 3-0 home defeat by Manchester United in the league his final game with Spurs.
The decision comes after a 3-0 home loss to Manchester United at the weekend left the London side eighth in the table.
United came into the contest on the back of a 5-0 hammering by their bitter rivals Liverpool but goals from Ronaldo, Edinson Cavani and Marcus Rashford sealed a comfortable win.
Goals by Emile Smith Rowe, Pierre-Emerick Aubameyang and Bukayo Saka crowned a majestic first-half display by Arsenal who were sharper and hungrier than a listless Tottenham side.