In a match where chances were rare commodities, Rafa Benitez's side were worth all three points and closed the gap on on second-placed Manchester City against the poor Canaries
The hosts started the game well, enjoying lots of possession, but their inability to carve open chances saw them pay as Juan Mata gave Rafa Benitez’s side the lead just before half-time.
Chelsea’s control continued after the break, forcing Norwich to play on the counterattack but, with neither side creating too many opportunities, a host of goals never looked likely.
Despite the rather hectic Christmas period, both sides made just two changes. For Norwich, Steven Whittaker and Steve Morison dropped out for Russell Martin and Grant Holt while, on the back of their 8-0 hammering of Aston Villa at the weekend, John Obi Mikel and Oscar replaced Frank Lampard and Eden Hazard for Chelsea.
The first half was a very tightly contested affair, but Norwich certainly began the more promising, stringing together a good number of passes in the Chelsea half, but the visitors’ defence remained solid.
Norwich looked to have been played in when Chelsea poorly cleared a Javier Garrido cross, but Alex Tettey’s half-volley tumbled out for a throw in.
Around the half-hour mark, Chelsea began to take control as Mata started to see more of the ball but they were still struggling to create chances with Norwich defending well.
However, in the 38th minute, Oscar did well to retain possession in the centre before finding Mata on the edge of the box, and the Spaniard smashed an effort into the far side of the net to open the scoring.
Bradley Johnson flashed a near-post header just over a few minutes later, but Chelsea went into half-time with a deserved 1-0 lead.
The second half started were the opening 45 minutes left off as Chelsea controlled possession and looked comfortable, knocking the ball around in a confident manner, while Norwich attempted to spring counterattacks.
Hoolahan seemed Norwich’s best bet of getting back into the game, but often the only pass on was forward to Grant Holt, but either the Chelsea defence would halt the striker, or he strayed offside.
The visitors continued to control the match, but for all their possession they could not get past the Norwich defence, much like their hosts in the first period.
Benitez’s decision to introduce Lampard and Hazard helped create a bit more dynamism in the final third and Mata could have got his second as he headed just wide from an Azpilicueta cross.
But, come the full-time whistle, Chris Hughton's charges could not assert themselves enough on the dominating Chelsea to carve out a valuable equalier, and slump to their second defeat on the trot after going 10 games unbeaten.