An early goal from Grant Holt raised hopes of a shock at Stamford Bridge. But clinical finishing from the European champions left Norwich City well beaten.
Fernando Torres, Frank Lampard, Eden Hazard and Branislav Ivanovic put them to the sword.
Chelsea looked stunned as Norwich took the lead in the 11th minute thanks to three of the players recalled by Chris Hughton.
Terry was hurt defending a free-kick and he was still hobbling when Wes Hoolahan was allowed to cross to Leon Barnett, whose knockdown was crashed home by Holt.
But within 11 minutes, Chelsea had turned the game on its head.
Torres made amends for his earlier miss by timing his run to perfection to head home Branislav Ivanovic's cross and although Alex Tettey might have restored Norwich's lead on his full Premier League debut but for a completely misjudged header of his own, the visitors then pressed the self-destruct button.
They failed to clear their lines in the 22nd minute and were horribly deep as Torres' overhead kick rebounded to Lampard to arrow home first time from 18 yards.
The poor defending continued when Cole headed wide, and hit a new low in the 31st minute as Terry cleared a corner, Mata evaded a lame tackle and was allowed to run unchallenged for 60 yards before threading in Hazard to slot home.
It could have been even worse for the visitors, with Cole's shot blocked behind and Oscar brilliantly dancing through but scuffing his finish straight at John Ruddy.
Holt beat Terry to two headers - both just off target - either side of half-time to serve notice that the game was not quite over.
It might have been had Hazard been awarded a penalty after a clumsy challenge from Barnett or had Oscar's 20-yard stinger been out of Ruddy's reach.
Ruddy also came to the rescue to thwart Mata after the winger's superb run onto Hazard's pass as Chelsea really began to turn on the style.
Lampard was replaced by Ramires midway through the half, with Norwich sending on Anthony Pilkington for Bradley Johnson.
The visitors looked happy simply to avoid a drubbing and they held out for most of the half, with Ruddy winning another one-on-one battle with Torres.
But he was beaten again 14 minutes from time when Ivanovic smashed home a superb near-post volley from Mata's lay-off, yet another assist for the red-hot winger.
A raft of further substitutions followed but a fifth goal did not, despite Chelsea looking like they could score at will.