Clint Dempsey headed in a late equaliser for Fulham to dent Chelseaâ€™s title hopes heading into 2009.
Fulham had taken the lead early in the first half from a free kick, Dempsey knocking in the first of his two goals from close range.
Lampard equalised just after half time when Schwarzer dropped the ball in the box, leaving the England international with the easiest of goals.
Chelsea were a different side compared to the one seen in the first half, and a second goal seemed to be a question of when, not if.
Lampard provided it with a swerving free kick that flew into the corner past Schwarzer.
But more drama was to follow. Fulham won a late corner and Dempsey rose to head home an unlikely equaliser.
After a busy period of games, Luiz Felipe Scolari opted to shuffle his pack, drafting in Deco and Florent Malouda, and leaving Nicolas Anelka on the bench.
The Blues knew that the pressure was on after Liverpoolâ€™s impressive 5-1 demolition of Newcastle, and they started well.
Lampard and Drogba both tested Schwarzer with shots, but some sloppy marking caused Chelsea to go behind after 11 minutes.
Dempsey was allowed to chest the ball from a free kick and poke the ball past Cech and into the net.
Drogba had his second attempt of the match on 19 minutes, skimming a shot across the face of goal after being fed by Mikel.
Chelsea were forced into a change just after the half hour mark with Malouda unable to continue due to a hamstring problem.
Anelka took his place and made an immediate impact, unleashing a shot that was kept out by Schwarzerâ€™s leg.
Ricardo Carvalho was forced into action for the first time in two months as Chelsea suffered another injury, this time to Brazilian defender Alex.
This didnâ€™t interrupt Chelseaâ€™s rhythm however, and Lampard had two more efforts on the Fulham goal before the half was out.
Within minutes of the restart, Lampard had his goal. Aaaron Hughes and Schwarzer got into an almighty mess and the ball broke loose to Lampard, who had the simple task of tapping the ball in.
The away side began to crank up the pressure in search of a winner, but a combination of Schwarzer and some wayward finishing kept the scores level.
Scolari made the slightly questionable decision to take off Joe Cole - one of Chelseaâ€™s better performers - on 72 minutes, but such thoughts were quickly forgotten as Lampard scored his second goal of the afternoon to give Chelsea a deserved lead.
The England midfielder lined up a free kick 25 yards out and crashed in a drive that swerved away from the despairing reach of Schwarzer.
Fulham seemed unable to muster a response, and Chelsea looked set to play out time and secure a vital victory.
But some more sloppy marking put paid to that idea. Simon Daviesâ€™ corner was met by Dempsey, whose header went in with Petr Cech a mere spectator.
Craven Cottage went wild, and Luiz Felipe Scolari was left to count the cost of a second successive draw away from home, a result that leaves his side three points behind Liverpool.