It might have been a dour affair at Stamford Bridge, but it didn't matter as Olivier Giroud's first-half header put the Blues four points clear in third-position on the Premier League table.
Norwich, already consigned to playing in the Championship next season, lost no respect for their performance and almost entered the break with a clean-sheet.
Speaking after the game, Giroud said: "We needed to be patient and move the ball quick against a team who play a deep block. We created a lot of chances but it was important to score before half-time.
"We should have scored more goals as we had a lot of possession. The team was a bit under pressure also because we know we needed the win definitely so we are happy."