Jose Mourinho's side moved four points clear of second-placed Arsenal before their London rivals hosted Sunderland later in the afternoon, but they left it late to seal the three points against a highly-skilled and adventurous visiting team.
But Distin lost Terry at the goal as the home side somehow escaped with three points they barely merited having spent the afternoon firing efforts from long range at the visiting goal.
It is a cliche, but prospective champions win matches while not playing well. Which just about summed up Chelsea's afternoon.
PRE-MATCH: Late change to the Everton team with Steven Naismith having to step in for Lacina Traore, who pulled up injured in the warm-up.
11' - OSMAN GOES CLOSE: Everton have been pinned back, but Howard is yet to make a save of any note. Osman then unloads a fabulous hit from 25 yards. Nice tip over by Cech.
28' - SMART SAVE FROM HOWARD: Cesar Azpilicueta with a powerful shot at the Everton goal, but that is a solid piece of goalkeeping by Howard to make the stop.
56' - CECH SHINES AGAIN: Coleman with a lovely little pass to Osman. His shot takes a deflection off the heels of Mirallas. Cech nudges it wide. Fine save.
59' - DOUBLE SAVE! Brilliant save by Howard to halt the Ivanovic volley after he was forced to dive to left to prevent the Hazard shot from hitting the net. Superb piece of goalkeeing.
90+2' - GOAL! Terry pops up to force the ball into the net from the Lampard free-kick. Terry gets a touch to it. Howard can't hold it. And Chelsea lead 1-0. What a vital goal that could be.
Chelsea have recorded their 150th win in all competitions under Jose Mourinho (both spells).
Chelsea are now unbeaten in 23 Premier League home matches, and 12 in the PL (home and away). Everton are now winless in five Premier League away matches, and have lost their last three in the Premier League.
Frank Lampard scores his sixth league goal against Everton, all for Chelsea. Only Didier Drogba (seven) scored more against Everton for Chelsea in the Premier League than Lampard. Jerrel Hasselbaink and Gianfranco Zola also scored six league goals vs Everton for Chelsea.
Was Everton goalkeeper Tim Howard at fault for the winning goal? Perhaps the visiting goalkeeper should have done better, but was difficult to grasp the free-kick from Lampard such was its accuracy. Distin and Jagielka will be just as disappointed about nodding off having done their work to keep the home side quiet all afternoon.
MAN OF THE MATCH
Sylvain Distin (Everton): Just keeps getting better and better in central defence for a highly impressive Everton side. So unfortunate to be on the losing team.
Chelsea: Cech 7; Ivanovic 7, Cahill 7, Terry 8, Azpilicueta 6; Lampard 6, Matic 5; Willian 5, Oscar 5, Hazard 6, Eto'o 5...subs: Ramires 7, Schurrle 6, Torres 5
Everton: Howard 7, Baines 7, Distin 8, Jagielka 7, Coleman 7, Barry 8, McCarthy 7, Pienaar 6, Osman 6, Mirallas 6, Naismith 7..subs: McGeady 6, Deulofeu 6, Barkley 6
THE MATCH IN A TWEET