The Hammers were heading for a place in the top four until Fabregas equalised with a penalty a minute from time after Michail Antonio brought Ruben Loftus-Cheek down, but replays showed the contact was outside the area.
Manuel Lanzini had put West Ham ahead with a fine effort from range, before Fabregas equalised late in the opening period with a 25-yard free-kick.
West Ham travelled to Stamford Bridge this weekend confident of heaping yet more misery on a Chelsea side which have exited the Champions League and FA Cup.
Chelsea are 10th with nine games to play after climbing from perilously close to the relegation zone a week before Christmas.
West Ham are fifth, two points behind fourth-placed Manchester City, and take their quest for the top four and Champions League qualification across London.
The Blues were knocked out of the Champions League by Paris Saint-Germain and FA Cup by Everton last week, but the ailing champions will be aiming to finish the season on a high.
Guus Hiddink will be without striker Diego Costa, who is suspended for the game following his red card against Everton last weekend, while the Dutchman will also have to do without Eden Hazard, who has ongoing hip and groin problems.
Alexandre Pato could make his long-awaited debut in Costa's absence, but Radamel Falcao (thigh) is continuing to find fitness and defender Kurt Zouma (knee) is out for the season.
West Ham defender James Tomkins was expected to resume full training this week but will miss Saturday's trip.
Tomkins is recovering from a calf injury and, like James Collins (hamstring), is anticipated to be available following the international break.
On-loan Chelsea winger Victor Moses is ineligible to face his parent club, but Sam Byram comes into contention after being cup-tied for last week's draw at Manchester United.
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