Lampard drove home the winning goal 18 minutes from time after Didier Drogba had cancelled out Louis Saha's opener within the first 30 seconds of the game for the Toffees.
Interim Blues head coach Hiddink, in his last game in charge, left Michael Ballack on the bench, with Drogba and Nicolas Anelka both starting.
Phil Neville and Steven Pienaar both shrugged off knocks to start for the Toffees, with Saha handed the task of being the lone striker.
The game exploded into action within 30 seconds of the first whistle, with Everton taking the lead through Saha.
A ball into the area was not properly cleared by the Chelsea backline and Marouane Fellaini's header fell to Saha, who rifled home a superb left-foot drive from 15 yards.
Hiddink's side were clearly rocked by such an early setback and it took them 14 minutes to find an opening, as Michael Essien shot over from the edge of the area.
However, with 21 minutes on the clock Florent Malouda found space on the left and his pinpoint cross was met by Drogba, who powered home his unmarked header from eight yards.
From that point on Chelsea started to dominate the play, but rarely threatened Tim Howard, with Joleon Lescott a rock at the heart of the Toffees defence.
Just before the break Ashley Cole broke forward from left-back and tried a shot from a narrow angle, but it didn't trouble Howard at his near post.
David Moyes brought on Lars Jacobsen to replace Hibbert at right-back for Everton at the interval, but Chelsea continued to have the better of the game.
On the hour mark, Lampard released Anelka and he almost gave his side the lead, as he lifted a shot over Howard but a couple of feet past the far post.
Seven minutes later Everton had their best chance since the opening minute as Leighton Baines curled in an excellent cross from the left and Saha headed over from ten yards out.
Lampard made them pay for that miss with 18 minutes left to play, turning away from Neville and driving in a left-foot shot from just over 20 yards which just beat the despairing dive of Howard.
Malouda came close to sealing the win with just over ten minutes to go, as his 30-yarder bounced down off the underside of the crossbar and out with Howard well beaten.
Anelka had the final chance of the game in stoppage time, but under pressure from Lescott the Frenchman lifted his shot over the crossbar, but it mattered little as the final whistle sounded.