Pedro’s brilliant strike and goals from Gary Cahill and Willian secured Chelsea’s fourth win in their last five league games, sparking jubilant celebrations from Conte and his players.
But while the Blues made their way back to London, Tottenham were securing a crucial victory over Arsenal that keeps them firmly in the hunt.
With four games remaining, Chelsea have a four point advantage over Tottenham and Mauricio Pochettino’s side can temporarily trim that gap to one point if they win at West Ham on Friday, before the leaders host Middlesbrough on Monday.
Conte knows it would only take one slip to give Tottenham real hope of overhauling them and he cautioned his players against thinking the race is over, even if they do have an easier run-in than Spurs.
“It is a great win but at this part of the season every win is a great win for us,” he said.
“For this reason we must celebrate in the right way, with my players, with the staff, with our fans.
“We have to have great enthusiasm and great patience because we are having a great season but to become a fantastic season we must win (the title).
“The message to the players was not words. Only hugs and enthusiasm.
“Now it’s important for us to prepare the right way for the next game. If we don’t win against Middlesbrough then you lose this great win.”
Recent defeats against Crystal Palace and Manchester United had the critics questioning whether Chelsea were set to stumble with the title within touching distance.
But they have recovered impressively, with last weekend’s FA Cup semi-final win against Tottenham followed by league victories over Southampton and Everton.
– ‘Kill the game’ –
On paper Chelsea appear to have a smooth path to the title as, following the clash with lowly Middlesbrough they face West Bromwich Albion, Watford and relegated Sunderland.
Conte tried his best not to look too far ahead, but even the cautious Italian couldn’t completely hide his joy at a result that moved Chelsea a step closer to being crowned champions in his first season.
“For sure it’s a great result for us. To win at Everton is not easy. My players showed me great patience to wait for the right moment to hit,” Conte said.
“It was important to keep the clean-sheet after a few games without one. That’s good for our confidence.
“We finished a crucial week very well. We all know there is this part of the season that is more important.
“We are having a fantastic season, but we must be calm. I don’t know how close we are to the title.”
After winning their last eight home league games, Everton were by far the strongest opponents left on Chelsea’s schedule and for 60 minutes they lived up to that billing.
In the end, they crumbled under the pressure of Chelsea’s relentless probing and Everton manager Ronald Koeman admitted the Blues have the look of champions.
Asked if Chelsea have title quality, Koeman said: “Yes, especially in the last 30 minutes. They are confident in having a good defence.
“They wait for chances and are really clinical. Without playing on the highest level, they still won the game because they have that attacking quality.
“One of the most difficult things is to create chances because they have a difficult system to play against.
“When they get a little more space they kill the game.”