The Ivory Coast international, who will soon head out to Cameroon, scored his sixth goal in just 10 appearances for the Clarets, which is the most by an African player in their first 10 games since Pierre-Emerick Aubameyang in April 2018.
The ex-Lyon forward, 25, drew the foul from Diego Llorente before getting to his feet and dispatching the resulting free kick past Leeds United goalkeeper Illan Meslier as Sean Dyche's side were beaten 3-1 at Elland Road.
Cornet had pulled the visitors level against Marcelo Bielsa's Whites, netting Burnley's first free kick in four years, when Steven Defour swept the ball past Manchester United stopper David De Gea at Old Trafford.
That, however, was as good as it got for the away side, who had trailed at the break after Jack Harrison punished James Tarkowski's error in the 39th minute.
The 25-year-old midfielder was denied by Wayne Hennessey with his left foot but converted the rebound with his right.
Stuart Dallas side-footed Leeds United into the lead in the 77th minute when the Clarets were slow to respond to a quickly-taken corner before substitutes Joe Gelhardt and Daniel James combined to wrap things up deep into stoppage time.
Here are the ratings.
9. Johann Berg Gudmundsson 4
Withdrawn at half-time and replaced by goalscorer Cornet after a relatively anonymous first half showing. Ayling had the Icelandic winger tied up, giving Dallas the licence to spread his wings. The Clarets need more from the ex-Charlton Athletic man.
10. Aaron Lennon 5.5
Showed the right attitude and mentality, stayed committed to the cause, worked hard, but the ball didn't stick around long enough for the ex-England international to get on it and have a say on Burnley's play in the final third. The winger, on his return to Elland Road, was quiet when switched to the right flank.
11. Chris Wood 4.5
The striker is finding the positions to expose opposition defences, but he's failing to convert good openings at key stages of the game. The New Zealander should have opened the scoring at Elland Road, just as he should at Old Trafford, and struggled to make the ball stick.
12. Maxwel Cornet 7
Another sprinkle of magic from the Ivorian drew Burnley level as Meslier couldn't get within reach of his perfect set-piece. He also went close with an improvised flick from a corner. He'll be sorely missed when he departs for the Africa Cup of Nations.