Verstappen secured pole position at the Hungaroring by less than two-hundredths of a second ahead of Mercedes' Valtteri Bottas.
The strong result in qualifying comes only six days after Verstappen's strong display at the German Grand Prix, where he took his second win of the season.
"It's been a good week so far," Horner told Sky F1. "For Max to get that pole, it's fantastic for him, what a fantastic lap. I was hoping that his first lap in Q3 was going to be enough, and was hoping the circuit wouldn't get quicker.
"But it was obvious that he needed to improve, Bottas was coming and getting closer and closer. It really came down to the last two or three corners for Max to nail the lap."
Horner also praised Honda, who he says is continuing to deliver, despite Hungary not being one of the most power-sensitive circuits on the calendar.
"Honda is doing a super job and all credit to them for giving us the engine to get us on pole today," Horner added. "The track layout is less power-sensitive then others that we go to, but these motors are starting to come to us now.
"Progress is being made in all areas, the chassis has been working well, the engine has been working well and of course, Max has delivered some incredible laps.
"We're definitely making progress, Austria we won, Silverstone I thin we should have been second on the road, we won the last race and now a pole position here."