The Chelsea captain sealed the win when he pounced on a Frank Lampard cross into the six-yard box and poked it home a split-second before Everton keeper Tim Howard arrived.
The victory moved the London side four points clear in first place with 60 points pending the outcome of the match between Arsenal and Sunderland later in the day. Everton remain sixth on 45 points.
Everton looked the better side for most of the scoreless first half although neither side had many quality chances. Chelsea in particular failed to connect at midfield and advance the ball profitably.
The hosts came out with more energy in the second half, with Ramires replacing Oscar, and Howard faced some stiff tests in the visitors' net.
Fernando Torres was brought on for the Blues after 62 minutes to add another offensive threat. Skipper Jose Mourinho might have been mindful that Torres scored the winner when Everton visited Chelsea last season, but the Spaniard proved ineffective.
Entering Saturday's contest, Everton had not won a Premier League match at Stamford Bridge since 1994, but the Liverpool side did beat Chelsea 1-0 at home back in September.
Chelsea were unbeaten in 11 league matches entering the game, but fell to Manchester City in the FA Cup last weekend. Skipper Jose Mourinho is now unbeaten in 74 top-flight home games in charge at Stamford Bridge.