Morata headed the opener past goalkeeper Kasper Schmeichel shortly before half-time, and Kante doubled their lead after the break.
They looked really solid today in a 2-1 win at Leicester City, and find themselves just one point behind the two Manchester clubs for the top of the table.
'Thibaut gave me the ball, I had time so I went on a run and shot.
That miss proved costly for Shakespeare's side as, less than two minutes later, Chelsea found the breakthrough.
Chelsea then had a penalty shout of their own after a tangle between Gray and Victor Moses, but the referee waved the appeals away, and play continued.
GETTY Vardy said it will be tough for former teammate Danny Drinkwater at Chelsea
The Toffees have spent big on recruits with Jordan Pickford, Michael Keane and Gylfi Sigurdsson all arriving for huge sums of money, as well as Davy Klaassen and Sandro Ramirez.
Chelsea continued to create problems for Leicester but lacked the final touch and Leicester nearly made them pay when Islam Slimani's shot was parried away by Thibaut Courtois in the 40th minute.
Leicester, who slip to 17th, have now lost six of their last seven home games against Chelsea.
On rejecting Arsenal, who won the FA Cup last season, Vardy added: "It wasn't the Premier League was it?"
Here's a statement that I've longed to write for many years now: can't wait for the Chelsea tunnel cam (i.e. "fans view") to be released within the next 24-48 hours!
The away fan allocation at the ground is 3,000 and the chant, which has anti-semitic overtones, came after the Spanish striker scored the opening goal in a 2-1.