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.
1. Wayne Hennessey 5.5
Plunged to his post to make a smart save from Junior's flick in the first half before a poor throw handed Raphinha a shot on goal. Pushed Harrison's shot back into the midfielder's path for the opener, static for the second and didn't get enough on James's header to prevent the third.
2. Matt Lowton 5.5
Battled well with Harrison, but had more on his plate when the midfielder was replaced by speed merchant Dan James. Fought on after being struck in the face with a bottle, but caught out when failing to pick up the run of James from Gelhardt's cross.
3. Charlie Taylor 6
Recovered well after a shaky start on his old stomping ground as Raphinha hogged the touchline and exploited the space. Arguably Burnley's most creative outlet, particularly in the first half when teeing up striker Wood on a couple of occasions.
4. James Tarkowski 4.5
The defender's nonchalance proved costly - just as it did at Southampton earlier in the season - as the Clarets went behind just before the break. Caught under Ayling's delivery when Roberts went close and didn't get out to the ball in time to prevent Dallas from scoring.