Gasly showed improved form but was disappointed to not achieve a podium finish.
The good result has come off the back of a string of bad performances since the Frenchman's promotion to Red Bull at the season, such as qualifying only 17th in the opening round in Melbourne and more recently being lapped by teammate Max Verstappen in Austria.
"I think Pierre has done a very good job all weekend I think, and I think compared to the race in Austria, which really was a tough weekend for him, I think coming here, just focussing on what he's doing and going back to basics, he's been like a different driver all weekend." Horner said.
"From the first session he has been competitive, he built on that in P2 and through all three elements of qualifying he's been competitive and even the race here.
Gasly topped the time sheets for the first time in his F1 career during Friday's first practice session, going on to qualify fifth and ahead of Ferrari's Vettel for the race.
The former Toro Rosso driver also impressed when he pulled a daring move on Vettel around the outside of the Village corner to retake back the fifth place he lost out to the German driver off the line.
"I think his approach to the weekend definitely helped," Horner added. "He's just turned up here and has been competitive."