The three-time world champion, who leads Norris by 57 points in the drivers’ championship with five races remaining and 146 points up for grabs, suffered engine problems on Friday before bemoaning a lack of grip as he finished five-tenths off the pace in final practice .
But Verstappen strung it along in his only timed lap in the final qualifying session to claim second on the grid, less than a tenth ahead of third-placed Norris.
The pair had no answer to Ferrari’s Carlos Sainz’s brilliant lap, with the second Scuderia of Charles Leclerc – last weekend’s race winner – finishing fourth.
George Russell earned fifth place on the grid for Mercedes, one place ahead of team-mate Lewis Hamilton.
Verstappen was happy to put his Red Bull on the front row, especially after title contender Norris led the first two sessions of qualifying.
“To be on the front row is an amazing result for us,” said Verstappen.
“Yesterday was basically a complete write-off. We were behind and the car wasn’t feeling good. Everything was very difficult.
“So it was always going to be a tough qualifying, we made some adjustments and it started to feel better.
“I don’t expect miracles (about race pace). In Austin the Ferraris were really fast, the McLarens were competitive, so for my part I guess we’ll find out tomorrow.”
Mexico City’s Autodromo Hermanos RodrĂguez features the longest run on the Formula 1 calendar to the first pit stop – a 768m charge that could be critical when it comes to the title race.
Norris said on Thursday he would “adapt” his driving after being penalized for overtaking Verstappen off-track in Austin last weekend, hinting he may need to be more aggressive in certain situations.
That could be put to the test on Sunday if he is to get the better of Verstappen on the first lap.
Norris believes third place is a reasonable result and hopes his McLaren can provide strong pace for Sunday’s 71-lap race.
“I’m relatively happy to be P3,” he said. “I felt a little bit on the back foot and not that comfortable at all.
“We found some good sectors in qualifying. Q1 and Q2 were very good.
“I just couldn’t progress from there, the car was too difficult to drive in Q3. It’s too hard to get three tenths out of him compared to Carlos.
“But I’m happy with the third one. It looked like it could have been better, but I think we finished where we needed to be.”
Ferrari produced a dominant one-two at the United States Grand Prix, with Leclerc taking the win and Norris wary of the Scuderia’s speed.
“The last couple of weekends they’ve been faster than us. We weren’t at their level today, but tomorrow is another day,” Norris said.
“Ferrari were the guys to beat and Carlos is on top today. It will be a challenge to beat them tomorrow.
“Carlos will be fast and has nothing to lose. We will do our best, but I don’t think we have the speed compared to them at the moment.”
Norris will be without the support of team-mate Oscar Piastri after the Australian suffered a dramatic dip in form – crashing out in the first part of qualifying after being fastest in final practice just hours earlier.
In a blow to the McLaren constructors’ title bid, Piastri qualified just 17th and was joined in Q1 elimination by Verstappen’s team-mate Sergio Perez.
The Mexican, who admitted on Thursday he had endured a “terrible season”, disappointed his vociferous support at home by finishing 18th as pressure on his future at Red Bull intensified.
McLaren leads Red Bull by 40 points, with Ferrari a further eight points behind.