Goals by Philippe Coutinho and Divock Origi either side of halftime had put Liverpool ahead after Benik Afobe struck early for the visitors, but once again Juergen Klopp's side dropped points against the supposed also-rans.
With City, without a win in four games, a further two points back in fourth, Guardiola's chief concern will be ensuring they keep above Arsenal and Manchester United in the scrap for qualification for next season's Champions League.
Sergio Aguero's equaliser yesterday - his 15th league goal of the season - looked to have given City the launch pad to increase Chelsea's jitters but Fernandinho's rash tackle on Pedro for a penalty which Hazard scored on the rebound meant Guardiola was outsmarted by Conte for the second time.
"We come here to Stamford Bridge and play the way we have, with huge personality. I'm a lucky guy to manage these guys," said Guardiola.
Arsenal moved up to fifth, four points behind City with a game in hand, after a 3-0 home victory over struggling West Ham United - a first win in four for Arsene Wenger's side.
It was not just an important night at the top.
Hull City's third win in four games - a 4-2 triumph over Middlesbrough with five goals coming before the break - saw them climb above Swansea and out of the bottom three.
Lazar Markovic, Oumar Niasse, Abel Hernandez and Harry Maguire were all on target to leave Boro looking favourites along with Sunderland to drop into the Championship next season. Sunderland are 10 points adrift of the safety zone while Boro are seven behind Hull.