The Blues legend volleyed in James Milner's cross to pull the Premier League champions level after Andre Schurrle had broken the deadlock and Pablo Zabaleta had seen red
Andre Schurrle applied a clinical finish to Eden Hazard's superb cross to give the Blues the lead on 71 minutes, shortly after Pablo Zabaleta had received a second booking for bringing down Diego Costa.
Costa then struck a post before Lampard, on as a second-half substitute, volleyed James Milner's cross beyond Thibaut Courtois with five minutes left to give the Premier League champions an unlikely equaliser.
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Manuel Pellegrini took the surprise step of handing Eliaquim Mangala something of a baptism of fire. The Frenchman made his debut in place of Martin Demichelis as one of four changes from Wednesday's defeat to Bayern Munich.
Diego Costa's hamstrings held up enough to see him lead Chelsea's line, bumping Didier Drogba back to the bench after a lacklustre show in their Champions League draw with Schalke.
The Spain striker's first contribution to the contest was a full-blooded 50-50 with Vincent Kompany that saw him come off second best after Yaya Toure had forced the first save of the game out of Joe Hart.
Though Cesc Fabregas and Nemanja Matic's influence in midfield increased, the visitors were unable to completely stem the flow of City attacks and were fortunate to see Fernandinho fail to properly connect with Aleksandar Kolarov's cut-back and Sergio Aguero half-volley an Edin Dzeko knockdown over the crossbar when he might have done better.
But neither side could find a breakthrough before half-time, despite Aguero and Costa getting brief glimpses at goal just prior to the break.
Mourinho will undoubtedly have called for more from his players during the interval, but City picked up where they left off following the restart.
Aguero tested Thibaut Courtois early on with a left-footed attempt from the edge of the box moments before just failing to control a cross into the box when a goal would have been the likely outcome.
The Argentine again was at the heart of things when his snapshot forced another Courtois save but Ramires was on hand to clear the rebound with Dzeko lurking.
City's hopes of making the most of the ascendancy received a significant blow with just over an hour gone, as Zabaleta received his marching orders after a clip of Costa's heels brought a second yellow card.
That forced Pellegrini into a reshuffle that saw Dzeko make way for Bacary Sagna but the addition of another defender could not prevent Chelsea taking the lead.
The visitors broke incisively from an opposition corner before Costa played Eden Hazard into enough space on the right-hand side to pick out a delightful low cross that Schurrle turned in at the back post.
Costa thumped the post from distance but the hosts responded to rescue an unlikely point in the most incredible of circumstances, Chelsea's record goalscorer Lampard turning home James Milner's smartly volleyed cross.
Lampard predictably refused to celebrate, but even went close to securing a winner as Chelsea's fine early progress was checked for the first time.