Raheem Sterling scored his first goals for Chelsea, giving the 10-man Blues victory over a Leicester side that has had a disastrous start to the Premier League season.
The £50m summer signing’s deflected effort looped into the top corner to put the hosts ahead 67 seconds after the break, before doubling their lead from Reece James’ inviting ball, much to Conor Gallagher’s relief.
Chelsea had been completely dominant until Gallagher was sent off just before halftime for a second booking in seven first-half minutes.
Vardy twice went close and Ayoze Perez struck the bar as the visitors pressed for a late leveller that never came, meaning Brendan Rodgers’ side have now lost three games in a row since an opening-day draw with Brentford.