As the Toffees delighted in Ramiro Funes Mori's stoppage-time goal, referee Mike Jones told Chelsea captain Terry the visitors' celebrations would lead to an extension of the seven additional minutes which had been announced.
And Terry's improvised finish in the eighth minute of stoppage time made it 3-3, although later Chelsea interim boss Guus Hiddink admitted his side benefited from an official error as the captain was in an offside position.
"I was thinking maybe four, five minutes (to go)," Terry told Chelsea TV.
"Then the ref jogged past me and said 'you've got seven and a bit (minutes) there, they've just over-egged their celebrations'.
"We knew we had enough time to create a chance or something
A couple of long balls into the box.
"Brana's (Ivanovic) up there, (Kurt) Zouma's in there and all kind of fighting, hoping it drops
It managed to drop.
"I'm delighted to get my first of the season, but more importantly to get the point."
The fallen Premier League champions fought back from two goals down - the first an own goal from Terry on his 700th club appearance - to level before the late drama.
When Cesc Fabregas' deflected effort followed Diego Costa's opportunist strike, which came after a mix-up between Tim Howard and Phil Jagielka, Terry thought Chelsea would go on to win.
But Costa went off with a shin injury and immediately was sent for a scan
The extent of the injury is still to be made public.
Terry described Costa's overall performance as "unbelievable".
"I think the goal summed him up really," the defender added.
"A ball over the top where realistically he shouldn't have won (it) or had a chance of winning (it), he wins the ball and slots it in.
"Even at 2-0 down he's the one going round and pushing everyone, kept stretching their defence and making runs in behind."
Chelsea, with Eden Hazard nearing a return to fitness following a groin problem, will be keen for Costa to be fit to play at Arsenal next Sunday.
The Blues remained unbeaten in seven matches since Jose Mourinho departed, but they have just one win in five league games under Hiddink.
Terry added: "Tough game
They're doing great at the moment
There's no easy games any more in the Premier League.
"We know we need to start winning football matches
Drawing's not enough to climb the table as quickly as we'd like.
"If we can do that at the Emirates that's the perfect place to start."
Half of Everton's 22 matches have now been drawn and Kevin Mirallas, who scored a fine second, rued the missed opportunity.
Mirallas told Everton TV: "Really disappointing
When you're leading 2-0 at Chelsea, you control the game, you play very well, you have many occasions (and) the game finishes 3-3..
It's the same as when you lose a game."
Everton boss Roberto Martinez railed against the decision to allow Terry's equaliser to stand.
But Mirallas did not wish to dwell on the final act.
"Okay, it's a bad decision, but this is football," the Belgium winger said.
And Mirallas wants a first league win of 2016 against Swansea on Sunday ahead of a good performance.
"(On) Wednesday we played very well against Manchester City, but only got one point," Mirallas said.
"We played very well against Chelsea, only one point
I prefer next week to play not very well against Swansea and to win the game."
Source : PA