Second-placed Manchester United, who have made a perfect start with three wins out of three, were playing at Stoke City later on Saturday.
Chelsea's workmanlike victory at the 2016 champions was described by Morata as a stepping stone in their bid to retain the title.
"The most important thing is we are not in the first place and we look forward to moving ahead in the table," the 24-year old Spaniard told Sky Sports.
"It is important to win here. Always against Leicester at this stadium it is very difficult to win. We were in a good position at 2-0 but suffered to the end."
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Chelsea dominated the opening half but nearly fell behind in the 40th minute when their goalkeeper Thibaut Courtois was forced to make a close-range save from Islam Slimani.
The Foxes were punished immediately as Cesar Azpilicueta delivered an excellent cross from the right flank for Morata to head past goalkeeper Kasper Schmeichel.
Schmeichel was at fault for Chelsea's second in the 50th minute when an innocuous-looking shot by former Leicester midfielder Kante from 30 metres sailed away from the Dane's late dive into the bottom corner.
"It is always special to play my old team," said Kante. "I had an amazing year here but when I come I try to win and today was important and I am happy to score.
"It is always a pleasure to score but I keep it inside because I want to respect my old team."
Jamie Vardy reduced the deficit with a penalty in the 62nd minute after he was tripped by Courtois but Leicester rarely looked like snatching a draw, with the visitors missing several chances at the other end.
Substitute Willian twice came close for Chelsea who were given a stoppage-time fright when a swerving cross from the right fizzed beyond Vardy across the face of the goal.
(Writing by Zoran Milosavljevic; Editing by Clare Fallon and Brian Homewood)
