Arsenal's grip on fourth isn't so secure because Tottenham, which beat Crystal Palace 3-0, is six points adrift but with three games in hand after coronavirus and snow postponements this month.
Like Villa manager Steven Gerrard, Palace counterpart Patrick Vieira began isolating this weekend after a positive test. Palace failed to get its match at Tottenham called off but the Premier League board on Monday did approve two postponements for Wednesday.
Leeds, which was due to host Villa, and Wolverhampton, which was to play at Arsenal, were deemed to lack enough players to fulfil the fixtures due to Covid-19 outbreaks.
Surging City
City has now won nine consecutive matches in its title defence to gain top spot and pull clear.
The early goal blitz saw Kevin De Bruyne and Ilkay Gundogan score from open play and Riyad Mahrez and Raheem Sterling net from penalties.
Leicester threatened a comeback when James Maddison, Ademola Lookman and Kelechi Iheanacho scored in 10 second-half minutes but Aymeric Laporte's header and Sterling's second eased City's path to victory.
Lukaku ends drought
Romelu Lukaku hadn't scored in the Premier League since the home game against Villa. A trip to Villa ended the drought that's coincided with injuries and a coronavirus recovery.
Lukaku was brought off the bench at halftime with the game tied at 1-1 after Reece James' own-goal was canceled out by Jorginho from a penalty for Chelsea.
Lukaku took 11 minutes to find the net after glancing in from Callum Hudson-Odoi's cross. A foul by Ezri Konsa to cut out Lukaku's run then led to another penalty that Jorginho converted in stoppage time.
North London wins
Tottenham is now six league games unbeaten since Antonio Conte took charge to revive the bid for Champions League qualification.
Lucas Moura scored one and set up goals for Harry Kane and Son Heung-min. Wilfried Zaha was sent off in the 37th when Palace was already trailing 2-0 after flinging his arms at Davinson Sanchez having already been booked.
"We have to continue to improve," Conte said, "to exploit the confidence that is going to improve us. We know very well, I know very well, we have a big job to do."
Arsenal's fourth consecutive league win came with a sparkling performance that saw Bukayo Saka score twice, Kieran Tierney net, Alexandre Lacazette convert a penalty and Emile Smith Rowe complete the rout in stoppage time.
Other matches
Brighton celebrated a first league win in 12 attempts to go above Leicester into ninth in the standings. Leandro Trossard and Neal Maupay scored in the first half to clinch a 2-0 win over Brentford.
West Ham was dislodged from fifth after losing 3-2 to Southampton despite twice coming from behind.
Mohamed Elyounoussi's opener was canceled out by Michail Antonio, and Said Benrahma leveled for West Ham after James Ward-Prowse's penalty.
Jan Bednarek's header in the 70th clinched Southampton's win.
