Chelsea were disjointed for spells but were back on level terms before half-time thanks to an unfortunate own goal.
A cross by Sterling, back in the starting XI after a virus, struck the knee of Belgium defender Ameen Al-Dakhil and looped over James Trafford into the net.
Chelsea then scored three times in a strong second-half showing to take the points.
Sterling, who has not featured for England since the World Cup, won a penalty after being fouled by Brazilian defender Vitinho, which allowed Cole Palmer to score his first goal for the Blues since moving from Manchester City.
The four-time Premier League winner with Manchester City then scored his side’s third with an arrowed finish after Conor Gallagher had spotted his run.
Play restarted after Sterling’s goal before referee Stuart Attwell stopped the game as a check by the video assistant referee (VAR) for a potential offside was continuing.
However, the goal was eventually allowed to stand.
Substitute Nicolas Jackson sealed the points with a spin and finish, with Sterling once again involved in the move.
Having won at Fulham on Monday, it is the first time Chelsea have secured back-to-back away wins in the Premier League since October 2022.
Credit: BBC Sports
