Former Liverpool boss Benitez was treated like a pariah in his first match in charge, although the Blues did at least keep their first clean sheet in 11 matches and denied City top spot in the Barclays Premier League.
Sergio Aguero wasted the best chance of a turgid game which began after Chelsea's stadium announcer was drowned out by jeers as he appealed for calm in order to pay tribute to former manager Dave Sexton, whose death was announced on Sunday.
There were also expletive-laden chants of "You're not wanted here", and signs reading 'Benitez out,' coupled with songs and banners hailing the sacked Roberto Di Matteo.
The atmosphere was not much better at White Hart Lane, where West Ham fans taunted Tottenham about the stabbing of one of their fans in Rome during a fiery London derby.
Jermain Defoe scored either side of half-time and Gareth Bale also found the net in a 3-1 win, with Andy Carroll scoring his first goal for West Ham, but the contest was marred by offensive chanting from the away end.
West Ham fans chanted "Viva Lazio" and sang the name of former Lazio and Hammers man Paolo Di Canio on several occasions, something that was hard to stomach for the home supporters who witnessed the horrifying attack on Spurs fans in Rome in midweek.
There was also a goalless draw at the Liberty Stadium, where Liverpool boss Brendan Rodgers felt his side had a perfectly good goal ruled out on his "emotional" return to Swansea.
The Northern Irishman was given a good reception by the home faithful, but he could not leave with the three points as the Reds failed to make the most of the superiority they enjoyed for much of the opening hour.
The closest they came to a goal was Jose Enrique's close-range first-half effort from Luis Suarez's delicate pass, but it was chalked off for offside by the assistant referee.
Southampton manager Nigel Adkins denied predecessor Alan Pardew a winning return to St Mary's as the Saints impressively beat Newcastle 2-0.
Pardew was Southampton boss for just over a year and led the club to the Johnstone's Paint Trophy, but says he was "treated harshly" and exited the club after just 13 months.
The 51-year-old returned to the club for the first time on Sunday but saw his former club take a deserved 34th-minute lead through captain Adam Lallana, who linked with Jason Puncheon to set up Gaston Ramirez for their second goal after the break.
Manchester United returned to the top of the Barclays Premier League with a 3-1 win over QPR.
Aston Villa climbed out of the bottom three with a deserved share of the spoils in a 0-0 draw against Arsenal at Villa Park.
West Brom earlier moved up to third spot after Simon Mignolet's howler in the lunchtime kick-off helped the Baggies beat Sunderland 4-2 at the Stadium of Light.
Wigan overcame Reading 3-2, Everton and Norwich drew 1-1 and Stoke edged Fulham 1-0.
Charlie Adam's 26th-minute goal secured Stoke a 1-0 win against Fulham at the Britannia Stadium, the Scotland midfielder the beneficiary of the knockdown after Peter Crouch comfortably beat Philippe Senderos in the air.
Barclays Premier League Sunday Results
Swansea 0-0 Liverpool
Southampton 2-0 Newcastle
Tottenham 3-1 West Ham
Report | Reaction
Chelsea 0-0 Man City
Barclays Premier League Saturday Results
Manchester United 3-1 QPR
Aston Villa 0-0 Arsenal
Sunderland 2-4 West Brom
Stoke 1-0 Fulham
Everton 1-1 Norwich
Wigan 3-2 Reading