Everton made life anxious for Tottenham when Romelu Lukaku made it it 2-1 with 10 minutes remaining, and pulled another back through Enner Valencia to trail 3-2 with a minute of stoppage time to go.
Harry Kane has a slight knock to his knee but he is expected to recover in time for the match.
Kane scored 25 goals in 37 games in the Premier League last season as Spurs finished in second place in the table.
On one hand, the likes of Daniel Sturridge matched Luis Suarez step to step in Liverpool's failed title bid during the 2013-14 season and while his finishing is still one of the best, injuries have hampered his game.
They were much improved after the break, helped by substitutions which prompted more attack-friendly tactical tweaks, but the Blues can ill-afford to give sides like Spurs a two-goal head start.
Mauricio Pochettino hailed his Tottenham Hotspur side's belief after seeing them reduce Chelsea's lead at the top of the Premier League to seven points.
It was his 19th goal in the Premier League this term, meaning he is now the outright top scorer in the division.
This prompted Spurs to wake up a bit and they nearly got a third goal when Kane was through on goal one on one with Robles but this time the keeper made a save as the striker tried to dink the ball over him.
Kane moved into top spot on England's scoring leaderboard as Tottenham claimed a ninth successive home league win. Yannick Bolasie and Muhamed Besic who suffered similar ACL injuries continue to recover from their injuries and they are likely to miss the rest of the season but Everton have more than enough player to cope without them. We are in a position where you can see we play very good football, exciting team, very good players.
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Both Belgian defenders were forced off during the 4-0 victory over Stoke City and, though it is hoped that both substitutions were merely precautionary, they are both slight doubts for the encounter with Everton.
Asked if it took them a while to practice, Alli said: 'Nah, it's quite complicated but I think we got the hang of it straight away'.
"Everton are doing well, they have very good players and it's a tough game for us".
"It's up to us to be there if they fail", Pochettino said.
Lukaku did manage to add to his record, taking his tally to nine goals in nine games and his 61st for the club, but it came from a rare Vertonghen error, slipping on the greasy turf with nine minutes to go.
"He has got every opportunity - with the games coming up we have got to win matches, so hopefully the goals will come from him".
"It's fantastic to make history with our supporters", said Pochettino.
The hat-trick was on.