Cesc Fabregas scored a dramatic penalty with one minute remaining as Chelsea fought back twice to draw 2-2 with West Ham at Stamford Bridge, denying the visitors the chance to move into the Premier League's top four.
Manuel Lanzini's magnificent strike had West Ham in front, but Fabregas scored with a free-kick just before half-time to level matters.
Slaven Bilic introduced Carroll and he converted Dimitri Payet's pass after 61 minutes to seemingly seal victory, but Fabregas intervened with a controversial late spot-kick that was awarded for Michail Antonio's challenge on Ruben Loftus-Cheek.
A win would have put West Ham fourth in the table ahead of the meeting between their two closest challengers for a Champions League spot – Manchester City and Manchester United – on Sunday.
Instead, they stay fifth and miss the chance to defeat Chelsea for the first time in 10 attempts at Stamford Bridge.
Fabregas' late strike ensures Guus Hiddink's men avoid what would have been a first defeat in 14 Premier League matches since Jose Mourinho's sacking last December after a 10-day spell that had also seen them crash out of the FA Cup and Champions League.
Loic Remy was handed just his second league start of the season in place of the suspended Diego Costa - with captain John Terry and Oscar also coming into the team - and the forward forced Adrian to get down and save with his legs from a tight angle early on.
But it was the visitors who opened the scoring in stunning fashion after 17 minutes when persistence from Diafra Sakho – one of the visitors' three changes – and Payet opened up space for Lanzini outside the area.
The Argentine did the rest, curling a magnificent strike past the despairing dive of Thibaut Courtois for his sixth goal of the season.
West Ham almost made it two when Sakho's pass was brilliantly flicked on by Payet, but Aaron Cresswell's tame finish was deflected wide by Branislav Ivanovic's block as a key chance went begging.
Willian was just off target with a long-range free-kick at the other end as Chelsea, who had physio Jon Fearn back on the bench for the first time since the Eva Carneiro controversy, looked for a way back into the match.
The equaliser arrived three minutes into first-half stoppage-time from another set-piece. Fabregas stepped up from just outside the box after Winston Reid was booked for a challenge on Oscar and delivered an exquisite strike into the top corner, with West Ham's protests that he had moved the ball back to ensure he had more room ignored by referee Robert Madley.
West Ham were inches away from re-taking the lead when a fast break led to Sakho playing in Cresswell, who lashed an effort against the crossbar from a tight angle.
Bilic brought on Carroll for Sakho and within 84 seconds of being on the pitch, the substitute scored.
A precise pass from in-form Payet sent Carroll through and his first-time, left-footed finish was not cleanly struck but had enough on it to bounce past Courtois.
John Obi Mikel and Fabregas both headed over from close-range opportunities, while the influential Spain midfielder saw an overhead kick fall inches wide as Chelsea tried to find an equaliser.
It was almost game over in the closing stages, but Carroll had a header dramatically cleared off the line from Payet's corner.
That proved decisive when Chelsea were awarded a penalty with one minute remaining. Substitute Loftus-Cheek surged through on goal and went down under pressure from Antonio, with Madley pointing to the spot despite furious West Ham protests.
Fabregas then stepped up and calmly sent Adrian the wrong way to claim a controversial point.