It was Chelsea's sixth straight win over City without conceding a goal, since Kevin Keegan's City beat Jose Mourinho's Chelsea at Eastlands in October 2004 with a Nicolas Anelka penalty.
While his European dream hangs by a thread, Sven-Goran Eriksson will also be waiting nervously for the results of a scan on Nedum Onuoha's shoulder after he was substituted following a collision with Michael Essien.
City rang the changes following their defeat at St Andrew's last weekend, with Sun Jihai, Javier Garrido, Dietmar Hamann and Darius Vassell replaced by Michael Ball, Michael Johnson, Martin Petrov, and Vedran Corluka.
The visitors arrived having shuffled their pack following their midweek defeat in Istanbul with one eye on the return leg at Stamford Bridge. Amongst the changes were former City players Anelka and Shaun Wright-Phillips.
The backlash from their Istanbul test began in the sixth minute for Chelsea when former City striker Anelka advanced down the right wing and crossed for Essien, who was running at the City defence from midfield. Richard Dunne moved to intercept the pass but could only pass the ball into his own net beyond Joe Hart.
While the goal served to separate the two sides in the first half, in truth, City had more chances in an open and eventful first 45 minutes in which both sides competed.
City were twice denied by deflections before half-time, once from Stephen Ireland's shot following Benjani's well-timed run and cross.
The other came when Michael Johnson and Ireland's one-two ended in Johnson's shot looping into the air off Juliano Belletti and Ashley Cole volleying off the line with Carlo Cudicini stranded.
The chances didn't end there for City though and the pick of Petrov's first-half efforts on goal was a rasping left-footed drive over Cudicini's bar.
Chelsea took control of the second half and made City rue their missed chances. Hart was alert to intercept Wright-Phillips' cross for Anelka in the 50th minute, but Salmon Kalou wrapped it up in the 53rd minute when Essien's pass fell to him and the forward ghosted through the City defence and rounded Hart to make it 2-0.
Frank Lampard's cross in the 55th minute found Anelka free of City's defence, but his measured header was tipped against the bar by Hart, who managed to grab the loose ball before it rolled over the line as Anelka closed in.