Verstappen, who has already forged a reputation for bold overtaking, pulled off the mid-race pass as both men were struggling with the tricky conditions to wrest second place from the championship leader, who later retook the position to narrowly beat the Dutchman into third.
"That move at Becketts... that was pretty sensational," Horner exclaimed.
"Hopefully we can build on this momentum - hopefully we get a little closer to Mercedes in Hungary than we did this weekend.
"In reality though our target is catching Ferrari - and theoretically the second half of the season should be stronger than the first for us. I think it will be a great battle with them. The most encouraging thing was how much quicker we were than them today in clean air."
Verstappen said his speed in the race's early stages, when the field was running on the intermediate tyre, was the biggest positive from a very encouraging day for the team.
"On the inters we had great pace," he reflected. "It was a shame I couldn't get past Nico in the beginning, I couldn't see and was having to lift on the straights to see the braking points.
"But I got past and was then closing on Lewis. Even [later] on the slicks, to finish only 8.2s behind, I think was a great result for us."
Rosberg, meanwhile, said he had relished the fight, adding: "[Verstappen] was a bit annoying out there! It was a good battle! I got him in the end and tried to hunt Lewis down, but it wasn't possible."
WATCH: Verstappen overtakes Rosberg around the outside at Becketts
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