City fell behind in the sixth minute when Victor Moses fired home from 20 yards for the first league goal conceded by Pellegrini's club this term.
Senegal forward Diafra Sakho netted the visitors' second from close-range in the 31st minute.
Belgium midfielder De Bruyne marked his first City start with a clinical finish in first half stoppage-time.
But a brilliant Adrian save from Nicolas Otamendi's header ended the hosts' winning run at five matches and lifted West Ham into second place.
At Stamford Bridge, Arsene Wenger was furious Mike Dean opted not to send off Diego Costa following a clash with Laurent Koscielny and the referee further infuriated the Frenchman when he dismissed Gabriel for kicking Costa and then showed Santi Cazorla a red card in the second half.
Chelsea made their numerical advantage count in the 53rd minute when French defender Zouma was left unmarked to head in a Cesc Fabregas free-kick.
Belgium midfielder Hazard guaranteed the champions' second league victory of the season in the 90th minute when his strike deflected off Calum Chambers to leave the Gunners without a league success against the Blues since 2011.
Teenage striker Anthony Martial further endeared himself to Manchester United's supporters with a nerveless brace as his side came from behind to win 3-2 at Southampton yesterday (Sept 20).
19-year-old Martial struck either side of half-time at St Mary's after Graziano Pelle had given Southampton a 13th-minute lead.
Juan Mata added a third in the 68th minute and despite Pelle scoring again, United held on for a victory that propelled Louis van Gaal's side up to second place in the Premier League table.
United's old rivals Liverpool continue to struggle, having seen their run of league games without victory extended to four following a 1-1 draw at home to Norwich City.
Daniel Sturridge made his first appearance since April after hip surgery and his side went ahead in the 48th minute when Danny Ings, a half-time replacement for Christian Benteke, drilled home his first Liverpool goal.
But Norwich equalised 13 minutes later courtesy of a deft lob by centre-back Russell Martin, whose preparations for the game were disrupted by the birth of his son the previous night.
Earlier on Sunday, Son Heung-min's first Premier League goal earned Tottenham Hotspur victory over Crystal Palace.
The South Korea international struck in the 68th minute at White Hart Lane, moments after Spurs goalkeeper Hugo Lloris had tipped a shot from Bakary Sako onto the post at the other end, to give the hosts a 1-0 win.
It was Spurs' first home win of the campaign and lifted Mauricio Pochettino's side to ninth place in the table, below Alan Pardew's Palace on goals scored.
Odion Ighalo kept Newcastle in the relegation zone as the Nigerian forward's double inspired Watford's 2-1 win at St James' Park.
Ighalo gave Watford a 10th minute lead with a low strike and he increased their advantage with his fourth goal in six matches in the 28th minute.
Newcastle ended a nearly 500-minute goal drought when Dutch defender Daryl Janmaat netted in the 62nd minute, but Steve McClaren's team were unable to avoid their third consecutive loss.
Ten-man Sunderland slipped to the bottom of the table after a 2-0 defeat at Bournemouth.
Eddie Howe's side raced into a two-goal lead inside the first nine minutes, with Callum Wilson striking in the fourth minute before Matt Ritchie smashed in a superb volley.
Saido Berahino came in from the cold to fire West Bromwich Albion to a 1-0 win at local rivals Aston Villa.
Leicester staged another impressive fightback to maintain their unbeaten record with a 2-2 draw at Stoke.
Everton's Kevin Mirallas was sent off for a foul on Modou Barrow in the final moments of his side's 0-0 draw at Swansea.
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