Eighteen-year-old French forward Wilson Odobert marked his first Premier League start by drilling low and hard past Robert Sanchez to send home fans into raptures at Turf Moor.
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.
This was a comprehensive showing by Mauricio Pochettino’s side as they rallied after falling behind to secure a confidence-boosting win heading into the international break.
Chelsea have found goals hard to come by, yet with Sterling running the show they had no such problems in attack in east Lancashire.
Sterling has been left out of a fourth successive England squad as the Three Lions get ready to play Australia in a friendly and Italy in a Euro 2024 qualifier.
Yet the 28-year-old sent a reminder to Gareth Southgate of his qualities by being involved in all of his side’s goals.
This was only Chelsea’s seventh top-flight win in the calendar year and they remain a work in progress under Pochettino, with Arsenal expected to provide a much sterner test when the two sides meet on 21 October.
But having gone into September’s international break with four points from four games, they now appear to be moving in the right direction with goals beginning to flow.
This win lifts Chelsea to 10th in the table with 11 points from eight matches.