They achieved that thanks to Didier Drogba's 32nd goal of the season.
The Ivorian striker hit the equaliser seven minutes after Everton had taken the lead through youngster James Vaughan.
But it was Everton's Lee Carsely who had the first chance when he let fly from 20 yards within a minute of the start. However, the ball fell invitingly into the midriff of Petr Cech.
Chelsea replied in kind through John Obi Mikel on four minutes. His 30 yarder forced a fine save from Tim Howard as the ball was pushed away for a corner.
It seemed the early part of the game was all about long-range shooting as Cech seized an excellent dipping 25-yard right footer from Vaughan.
Another by Manuel Fernandes almost caught Cech by surprise but he managed to collect the ball at the second attempt.
Drogba almost opened the scoring on 14 minutes but, after being fed the ball from Shaun Wright-Phillips, the Ivorian let fly a rasper of a shot from just outside the Everton penalty area, which inched just over the crossbar.
Salomon Kalou zig-zagged his way through the Everton rearguard before his right-foot shot was smothered by Howard.
A quick counter-attack on 28 minutes saw Howard scramble to his right to get to a low left-footed daisy-cutter from Joe Cole.
Chelsea started the second half with a degree of urgency but they fell behind to the classic counter-attack five minutes in.
Leon Osman ran towards the Chelsea area and squared the ball across to the left where Vaughan nipped in front of Khalid Boulahrouz and squeezed the ball home past Cech.
The game was almost beyond Chelsea's reach but for an acrobatic save by Cech two minutes later from an audacious overhead kick by Vaughan.
This galvanised Chelsea into attack and the deficit lasted five minutes before Drogba tucked home a right-footer past Howard from six yards after good set-up play by Wright-Phillips.
The goal produced an on-pitch protest from Everton boss David Moyes who was seething that a challenge on midfielder Mikel Arteta seconds before the equalier was not given.
Moyes was sent to the stands by referee Mark Halsey for the pitch encroachment.
Chelsea suffered a FA Cup Final scare when Mikel was carried off the pitch on 75 minutes clutching his hamstring.
Everton had the ball in the net two minutes from time through James McFadden but James Beattie was adjudged to be offside.
Everton's point also means they are in next season's UEFA Cup.