Chelsea axed the popular Di Matteo on Wednesday - hours after their Champions League defeat by Juventus which continued their poor run of results, and appointed the former Liverpool man for the rest of the season.
Benitez's arrival in the dugout shortly before kickoff was greeted by boos with home fans continuing to chant Di Matteo's name throughout the first half.
Chelsea, now without a Premier League win in five games, improved after a sluggish opening period but created few openings to test City keeper Joe Hart.
City, knocked off top spot by Manchester United's 3-1 win over Queens Park Rangers on Saturday, closed to within one point in second while Chelsea are fourth, five points behind the leaders.
Jermain Defoe's double, including a superb first-half strike, and Gareth Bale's goal just before the hour jolted Tottenham Hotspur out of the doldrums with a 3-1 London derby victory over West Ham United at White Hart Lane.
Southampton moved out of the bottom three with a 2-0 home victory over Newcastle United, ensuring an unhappy return to the south coast club for former Saints manager Alan Pardew, whose Newcastle side are struggling to match last season's exploits which carried them to a fifth-place finish.
Liverpool manager Brendan Rodgers was also unable to get one over former club Swansea City on his return to Wales as the Anfield side continued their mediocre Premier League start with a 0-0 draw at the Liberty Stadium.
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