Debutant Juan Mata scored deep into injury time as Chelsea left it late to secure an unconvincing victory over 10-man Norwich.
The Blues led through Jose Bosingwa's stunning 25-yard shot but Grant Holt levelled after a blunder by Hilario.
Frank Lampard's penalty made it 2-1 after Ramires was felled by keeper John Ruddy, who was sent off.
Mata slotted in to seal the win but Chelsea's day was marred by a head injury to Didier Drogba.
Drogba took a heavy whack in the face from Ruddy and crashed to the floor with the scores at 1-1, as the keeper looked to punch clear a teasing cross.
The big Ivorian laid motionless on the pitch and was finally taken off on a stretcher after lengthy treatment which resulted in 11 minutes of injury time.
Drogba needed a breathing aid and was taken to hospital, leaving the Blues with an anxious wait to discover the extent of the injury.
Lampard restored Chelsea's lead and in those 11 minutes of added time, Mata finally gave the hosts breathing space to end the visitors' hopes and cap a pulsating and eventful match.
But Chelsea's fans were no doubt hoping that - following their tense victory over West Brom last Saturday - Bosingwa's fabulous early strike would be the prelude to a routine win.
Despite a blistering start in which Ramires saw a fine, long-range effort tipped wide by Ruddy, Norwich posed a serious threat in an open and entertaining game and could easily have snatched all three points themselves.
Bosingwa was a key attacking threat for the hosts from the off, twice rampaging down the right flank before he gave Chelsea the lead.
The home side worked the ball down the left and Lampard moved the ball across to Bosingwa, who drove his shot across goal and in off the far post.
Norwich responded with commendable composure and more than matched the Blues for the rest of the half.
Holt narrowly failed to connect with an inviting cross from Wes Hoolahan and Chris Martin forced a decent block from Hilario, who also kept out the follow-up strike from Kyle Naughton.
Holt had a headed effort saved but after the interval, the burly striker was able to celebrate a goal courtesy of a terrible gaffe by keeper Hilario.
The Portuguese raced from his goal straight into Branislav Ivanovic, who could only head the ball up in the air for Holt to hook it cleverly into the unguarded net.
Almost from the kick-off Chelsea piled forward down the left and from the centre Drogba was poleaxed by Ruddy.
After play finally resumed it was the Canaries who looked more likely to grab the winner.
Substitute Steve Morison should probably have earned them maximum points when he raced onto Holt's ball over the top but the Welsh international hesitated and John Terry dived in to clear.
Chelsea boss Andre Villas-Boas threw on both Mata and fellow new signing Romelu Lukaku and slowly the Londoners regrouped and got on top.
Fernando Torres headed straight at Ruddy and the pressure told when Ramires was brought down by the keeper after a delightful through-ball from substitute Nicolas Anelka.
Norwich felt the contact was minimal but referee Mike Jones pointed to the spot and they were made to see out the closing stages of a game with 10 men for the second time in two league games.
Ruddy's replacement, Declan Rudd, was unable to stop Lampard's blasted strike and Chelsea then started to dominate.
Ivanovic somehow missed the target from six yards after a great dinked cross by Lampard before Mata finally broke Norwich's brave resistance, capitalising on Ritchie De Laet's error with the game well in to its 101st minute.
Chelsea manager Andre Villas-Boas:
"The 1-1 came against the running of the game.
"The impact of the 1-1 on the emotional part of the game is tremendous but, again, I'm very, very happy that the team is able to control their state of mind, to fight back, to show commitment and desire.
"We looked better overall in a 90-minute performance."
Norwich City manager Paul Lambert:
"I thought we were excellent, I really did.
"The penalty's turned the game. We could've been up 2-1, but I can't ask any more from the lads, the way they played. They came here and they thrived on it.
"We were up against a team that could potentially win the Premier League.
"I think Chelsea know they had a game."