Having qualified third, Sergio Perez scored a brilliant victory on the streets of the principality.
The Mexican jumped ahead of the Ferraris of Carlos Sainz and Charles Leclerc with good strategy calls around his pitstops on the drying track, and then nursed his graining slick tyres in the closing laps.
His teammate Max Verstappen moved from fourth on the grid to third at the flag, getting ahead of pole man Leclerc.
Horner said the team had responded well to the tricky conditions created by the wet weather at the start.
"I've always prided ourselves on us being an attacking race team," he said. "And we've always focused on trying to do the basics well, whether it's strategy, whether it's pitstops, thinking on your feet, and I think today was all about thinking on your feet and reacting to the situation as it happens around you.
"And I think that the whole team responded brilliantly well, and the drivers of course had to deliver their part."
Horner stressed that the key to Perez's success was judging the crossover from wet to intermediates, and then on to slicks.
"It was an incredible race," he noted. "We knew there was some rain around, but I don't think we expected it to be tropical, at the beginning of the race there. It was a little chaotic with the delays, tyres coming on the grid, off the grid, on the grid.
"But with the amount of rain that did fall, it would have been impossible to race in those conditions.
"So once the race finally did get underway, it was always going to be about the crossover, and getting that crossover right. And we went obviously, from the extremes, the inters, to the slicks, and we got those calls right today.
"And the pitwall did a great job, the strategists, particularly the guys in the pit lane, they had to turn around the double stops today and of course, Checo, his performance, on the in-lap, on the out-lap, particularly on the inter tyres, was stunning.
"And then likewise on the slicks, and then obviously he had to manage the rest of the end."
Asked if Red Bull had won the race or Ferrari had lost it with strategic calls, Horner conceded that it was a bit of both.
"Of course, we had to go out and win it. But we also capitalised on the mistakes that were made, the circumstances were the same for everybody and it was very tight between the two teams.
"Charles in the early laps seemed to have things pretty much under control, he had a buffer of his teammate behind him as well.
"At that point in time, it looked like Ferrari had the race in the bag, but I think we just reacted very well to the to the conditions and got the crossovers right, the double pitstop, etcetera, etcetera, it worked very well for us.
"We were debating whether you go straight from the extreme on to the slick, as we saw with Lewis [Hamilton], when it hurt us a few years ago with Daniel [Ricciardo], but we decided it was a quicker route to go through the inter onto the slick.
"And the power of the out-lap was enormous. And I think Checo absolutely nailed it."
