The ex-Royal Antwerp winger opened his account for the Clarets with a rasping effort in the fourth minute, which cannoned home off the inside of the post.
Former Burnley striker Nahki Wells equalised a few minutes before the half-hour mark when firing the ball home from close range after Vincent Kompany’s side had failed to clear their lines from a corner.
But hometown hero Jay Rodriguez proved to be the match-winner in the 67th minute as the striker’s glancing header from Johann Berg Gudmundsson’s delivery beat Daniel Bentley and nestled in the far corner.
The Clarets enter the international break in fourth spot in the Championship with 17 points.
Here are the player ratings.
1. Arijanet Muric 6.5
There's an argument to be had over whether the ex-Manchester City stopper could have done more to impose himself on the corner that led to the equaliser, but the goalkeeper's distribution was exceptional, he eased the pressure when claiming a couple of long balls late on, and he made important saves to deny City's leading scorer Tommy Conway and ex-Claret Nahki Wells in either half. Photo: Ashley Allen
2. Connor Roberts 6
Always looking to get on the ball, and was an option for both Arijanet Muric and Taylor Harwood-Bellis when the home side played out from the back, but often wanted to keep hold of the ball for too long and was forced to turn back towards his own goal to find a team-mate. Solid enough defensively. Photo: CameraSport - Dave Howarth
3. Jordan Beyer 7
The German defender was handed his debut and he didn't disappoint. Assured in possession, moved the ball with purpose, deceptively quick in short sprints for the ball, got stuck in and put everything on the line in the latter stages to ensure the Clarets came out with maximum points. It's still very early days, but his partnership alongside Taylor Harwood-Bellis is already showing plenty of promise. Photo: CameraSport - Dave Howarth
4. Taylor Harwood-Bellis 8
A very exciting prospect. The 20-year-old's levels of consistency are quite impressive. A tad unfortunate for the away side's equaliser, but he more than made amends for that over the course of the game. His distribution out from the back is exquisite, breaking the lines time and time again, and the Young Lion made two vital interventions to clear off the line from Joe Williams before applying a vital touch to take Andreas Weimann's cross away from Antoine Semenyo. Photo: CameraSport - Dave Howarth