City started brightly and led on 10 minutes when Fernandinho found Leroy Sane, who fired past Ben Foster.
Three minutes later, it was 1-1 when Gareth Barry chipped to Jay Rodriguez, who beat Ederson.
West Brom were not level for long. Sane found Fernandinho and his deflected effort went in off a post on 15 minutes.
Sterling doubled the lead, finishing a cross from Kyle Walker on 64 minutes, before Matt Phillips netted a late consolation.
The win means City have beaten the 10-match start of Chelsea in 2005/06 by goal difference and extended their lead to five points. West Brom drop to 15th.
WBA: 4 Nov v Huddersfield (A)
MCI: 5 Nov v Arsenal (H)