Meanwhile, Fernando Alonso's season - set to be his last in F1 - continued to wind down in unspectacular fashion as the two-time champion scraped into Q2 after a wobble and qualified in 12th.
Red Bull's lock-out of the front row promises a thrilling multi-car duel down to Turn 1, but as a priority Horner wants his driver to remain out of trouble and work together to keep their rivals at bay after the launch from the grid.
Last year's race victor Verstappen, 21, had dominated all three practice sessions and was on provisional pole before the final flying laps at the high-altitude Hermanos Rodriguez circuit.
Championship leader Lewis Hamilton of Mercedes, who needs to outscore Ferrari's Sebastian Vettel by five points to take his fifth title, was fifth ahead of team-mate Valtteri Bottas with Vettel seventh and his Ferrari team-mate Kimi Raikkonen eight.
"I knew it was in there somewhere, I just knew the pace was in the auto, Max showed that all weekend".
Asked if the issue meant he felt pole was always in doubt, he replied: "Let's say I was surprised I was first in Q3, because I didn't feel good at all".
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"I knew it was there somewhere. This is why I don't want to think too much - none of us want to think too much - about the championship, but just really concentrate on the task at hand".
"I still wasn't convinced it was the cleanest lap, but I've got to relax a little".
"I was struggling in the qualifying", last year's race Verstappen said.
"But we're here to try and compete, so we will do the best we can to have a real race".
"I am really happy with it", he said.
Immediately after qualifying, Hamilton was asked if he would take a cautious approach to Turn 1, and replied: "Well you saw what happened past year with the red vehicle behind, so I don't know. We will get a good tow from the two in front so hopefully I can gain a position".
A seventh-place finish will secure the Briton's fifth career title, matching the late Juan Manuel Fangio of Argentina for second behind only the seven of Germany's Michael Schumacher.