The Spain international broke the deadlock seven minutes before half-time to record his 13th goal of the season.
It turned out to be a valuable one as Rafa Benitez's side were able to close the gap on Manchester City, beaten 1-0 at Sunderland, in second place. Chelsea are now four points behind last season's title winners, and have a game in hand.
There was no place in the Chelsea starting line-up for either Frank Lampard or Eden Hazard even though both had scored in Sunday's 8-0 victory over Aston Villa, a record defeat for the Midlands side.
John Obi Mikel and Oscar replaced them at a time when a newspaper report had stated that Lampard, whose contract expires at the end of the season, had been told by the Chelsea hierarchy that he must find a new club in January.
It took a while for either side to fashion a chance and the first fell to Norwich but Alex Tettey miscued his effort from the edge of the box so much the ball ended up going out for a throw-in.
Chelsea's reply, which took 10 minutes to arrive, was hardly more impressive as David Luiz, playing in a defensive midfield role, blasted a long range effort well over the Norwich crossbar.
Mata saw a shot blocked by Sebastien Bassong as Chelsea began to threaten. Luiz's ball reached Ashley Cole on the left of the City box but Michael Turner was in quickly to block.
Another Luiz ball set Mata up on the other side of the Norwich box but the Spain midfielder fired wide of Mark Bunn's near post and found only the side-netting.
Mikel fired another shot over the bar following an elaborate build-up and Chelsea finally broke the deadlock in the 38th minute when Mata received the ball from Oscar and beat Bunn from 20 yards with a perfectly-placed shot.
Cole fired wide early in the second half and Fernando Torres, who had been very quiet, soon saw a shot on the turn blocked by a defender. Victor Moses was next to have ago but the angle was tight on the left of the box and Bunn was able to save.
Home hopes were boosted by a fine interchange between Wes Hoolahan and Grant Holt but the latter fired across goal and wide, and the flag was up for offside anyway.
It was not long before Norwich were back under pressure but Bunn made a comfortable save to keep out Mata's free-kick from 30 yards out and once again the goalkeeper was not required when Luiz blasted another long-ranger metres over his crossbar.
Moses could have made it 2-0 in the 68th minute when he chested down a cross from the right Cesar Azpilicueta to elude his marker but his first-time shot ended up thumping into an advertising hoarding rather than the net.
Azpilicueta was hurt at the other end as Bradley Johnson challenged with a high boot before Lampard replaced Mikel in the 73rd minute and Johnson was booked for a clear dive moments before being replaced by Jonny Howson.
Bunn made another quality save to deny Hazard, who had come on for Moses in the 79th minute, after a clever back-heel from Torres had opened up the Norwich defence on the left. Hazard, on as a substitute, was then booked for a cynical trip on Russell Martin.
Cole had to hack the ball away for a corner in front of his own goal as Norwich piled on some late pressure and Bassong headed over from the resulting corner. It was too little too late for the Canaries and Chelsea were not troubled again before the final whistle.