Manager Guus Hiddink's unbeaten Chelsea record survived after an amazing six-goal second half that saw his side fall two goals behind, fight back to 2-2 and then seemingly throw away the points with poor defending when Everton sub Ramiro Funes Mori netted in the 90th minute.
Just as the visitors were about to hail their first win in the league at Stamford Bridge since November 1994, Terry struck deep into stoppage time with a back-heeled goal that Hiddink and furious Everton counterpart Roberto Martinez agreed was offside.
"Seven minutes of injury time, the last action happens in 97 minutes 51 seconds and John Terry is two yards offside," Martinez told reporters, saying that he felt "anger, pure anger".
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Of referee Mike Jones, he added: "Maybe refs need a bit of help, the crowd should see it. But to have a player two yards off in the box is unacceptable. There is no explanation. It's a big, big error.
"It's heartbreaking for us, the referee was not up to it," said Martinez.
Hiddink, while praising the resilience of his team as they risked everything in a final push forward, said: "He (Martinez) is quite right, he was offside.
"Sometimes it's in our favour, I've seen it. Oscar touched the ball and John was offside but he made a beautiful goal.
"It was over the seven minutes but when Everton were celebrating their third goal we asked the fourth official to add a minute for that. That was fair, I think."
Hiddink's pre-match warning that Chelsea were not out of the relegation dogfight seemed to be underlined when Terry turned Leighton Baines' cross into his own net five minutes after halftime and Kevin Mirallas quickly doubled the lead.
Two goals in two minutes from Diego Costa, who capitalised on a Phil Jagielka mistake, and Cesc Fabregas, with a deflected shot, squared the match before Funes Mori latched on to Gerard Deulofeu's cross amid shambolic Chelsea defending.
"I'm very happy with the spirit of the team," Hiddink added. "Of course I'm not happy with the goals conceded but very happy with the attitude."
(Reporting by Ian Chadband, editing by Tony Jimenez)
