The Blues had lost four of their opening 14 domestic fixtures under the Portuguese coach, but successive 3-0 successes against Wolverhampton Wanderers and Newcastle United respectively had lifted the Chelsea supporters ahead of the arrival of the league leaders.
Roberto Mancini's side were unbeaten after a remarkable start to their attempt to win the Premier League title for the first time in their history, and the Italian chief signalled his intentions to attack Chelsea from the start by naming both Sergio Aguero and Mario Balotelli in a front two, with David Silva supporting from the left.
Mancini's ambition paid off as early as the second minute as the visitors silenced Stamford Bridge with an opening goal. Aguero slid the ball into the path of the onrushing Balotelli, who kept his composure to round Petr Cech to slot the ball into an empty net.
It had been a rapid start from the visitors, and eight minutes later, they came inches away from doubling their advantage when Aguero shook off the attentions of his marker before driving the ball inches past the far post.
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City were unlucky not to be awarded a penalty when Silva was felled by Jose Bosingwa, but the referee remained unmoved and despite being outplayed and out-thought by the leaders, Chelsea struck with 11 minutes remaining of the first half to net an undeserved equaliser.
John Terry played the ball out to Daniel Sturridge wide on the right, and the winger tricked his way to the byline before pulling the ball back for Raul Meireles, who volleyed the ball past Joe Hart from close range.
Chelsea had started to discover renewed impetus before the break and that continued when they returned for the second half, with Sturridge striking a half-volley over the crossbar after being found by Juan Mata's free kick.
Vincent Kompany had been fortunate to avoid a second yellow card for a challenge on Mata, but Gael Clichy had no such luck on 58 minutes. The Frenchman had been cautioned at the start of the second half, and a rash tackle on Ramires resulted in City having to cope with 10 men for the remainder of the match.
That dismissal forced a reshuffle from Mancini, who sacrificed Aguero to bring on Kolo Toure, but it couldn't halt Chelsea's momentum, with Didier Drogba just failing to make contact with Bosingwa's teasing cross.
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With 17 minutes remaining, Villas-Boas sent on Frank Lampard to add an extra threat going forward, but the Blues were being met by a firm resistance from City who were sitting on the edge of their own penalty area.
However, with less than 10 minutes left, the home side were gifted an opportunity to take the lead when Joleon Lescott was adjudged to have handled the ball inside the penalty area, and Lampard stepped up to fire the ball with authority past Hart.
City tried to respond by sending on Edin Dzeko, but Chelsea managed to negotiate the final moments to record a vital victory over Mancini's side, that cut their deficit to the leaders from 10 points to seven, but City missed out on the chance to extend their advantage at the top to five points.
Despite the enormity of their success over City, Chelsea failed to build on their triumph, and after winning just three of their following 12 Premier League fixtures, Villas-Boas was axed as boss at the beginning of March.
As for City, they recovered from this setback by defeating Arsenal six days later, and they ended the campaign by securing their first Premier League title in dramatic circumstances when Dzeko and Aguero both netted in added-on time against Queens Park Rangers to snatch the trophy away from rivals Manchester United.