Sterling had a hand in all four goals as the Blues soar to victory after falling behind early at Burnley.
Chelsea had earlier fall behind through 18-year-old French forward, Wilson Odobert, marking his first Premier League start by drilling low and hard past Robert Sanchez to send Burnley into raptures.
Chelsea were disjointed for spells but were back on level terms before half-time thanks to an 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, inspired by Sterling, then scored three times in a strong second-half showing to take the maximum points at Turf Moor.
Sterling 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 former Manchester City player then scored his side’s third with an arrowed finish after Conor Gallagher had spotted his run.
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. The win takes them to 9th place, below Manchester United which is a point ahead of them in 8th place.