Victory kept Chelsea ahead of Arsenal and Manchester City, who both also claimed wins on Saturday.
Chelsea looked set to drop points for the second successive league match before returning captain Terry popped up right at the death to turn home Frank Lampard's cross and leave unlucky Everton empty-handed.
That late drama in the day's early kick-off put Jose Mourinho's men four points clear at the summit ahead of the 3pm fixtures, but Arsenal and City both responded with home wins of their own.
They did so in wildly contrasting fashion though, unlike in midweek when they suffered almost identical 2-0 home defeats in their Champions League last-16 first legs.
Arsenal, fresh from being beaten by reigning European champions Bayern Munich, cruised to a 4-1 victory over Sunderland that took them back to within a point of Chelsea.
The game was all but over by half-time with Olivier Giroud netting twice before Tomas Rosicky made it 3-0 in the 42nd minute.
Arsene Wenger's men did not stop there and Laurent Koscielny added a fourth before third-bottom Sunderland pulled a late consolation back through Emanuele Giaccherini.
Manchester City, however, did not have it nearly as comfortable against their former manager Mark Hughes' Stoke.
Looking to bounce back from their European loss to Barcelona, Manuel Pellegrini's men were frustrated during a goalless first half and were indebted to a 70th-minute strike from Yaya Toure - his 13th league goal of the season - to get the 1-0 win.
City, who play Sunderland in the Capital One Cup final next weekend, remain two points behind Arsenal but have a game in hand.
At the other end of the table, Fulham came within four minutes of a much-needed victory in new manager Felix Magath's first game in charge, only to have to settle for a 1-1 draw at fellow strugglers West Brom.
The Cottagers looked set to climb off the foot of the table after taking a 28th-minute lead through Ashkan Dejagah but they were denied a first victory in eight league and cup games by an 86th-minute equaliser from Matej Vydra.
That goal kept Fulham in last place but they are now only a point behind Cardiff after Ole Gunnar Solskjaer's men were thrashed 4-0 at home by Hull.
Nikica Jelavic notched twice for Steve Bruce's side, between goals from Tom Huddlestone and Jake Livermore, as Hull moved six points clear of 18th-placed Sunderland .
Visiting Southampton took an eighth-minute lead through Maya Yoshida but West Ham replied with goals from Matt Jarvis, Carlton Cole and Kevin Nolan to secure their fourth successive win.
The England forward signed a fresh £300,000-a-week deal on Friday and, after being on the periphery for much of the game, thrashed in United's second as they recorded a 2-0 win over the Eagles to move sixth in the table.
Rooney had not scored since another sweetly-hit strike in the 3-2 comeback victory over Hull on Boxing Day but he pounced six minutes after a Robin van Persie penalty to secure the points for the champions.