Verstappen scored his 14th win of the season for Red Bull but was kept honest by Lewis Hamilton through the opening stint as Mercedes opted for a different starting tyre.
While Red Bull fitted softs to both Verstappen and Sergio Perez's cars from the start, Mercedes went for mediums with Hamilton and George Russell, favouring a one-stop strategy.
Hamilton kept within two seconds of Verstappen through the opening stint before taking the lead when the Red Bull pitted, stretching out his mediums to last 29 laps.
But when Hamilton switched to hard tyres, the seven-time world champion said he was not feeling as comfortable, allowing Verstappen to extend his lead and ultimately avoid a second pit stop en route to victory ahead of the Mercedes.
Russell asked Mercedes at one point during the race to go for softs in the final stint, only to be told it would have required a long medium-tyre stint.
That approach was successfully taken by Ricciardo and McLaren, who pitted on lap 44 to switch from mediums to softs before going on a late charge that led him to seventh even after a 10-second time penalty was applied.
Mercedes team principal Toto Wolff said after the race it was "always easier to judge" with hindsight, but explained that the team's pre-race data suggested it had gone for the right strategy.
"I think the one-stop, medium-hard, looked like the right strategy," said Wolff. "That the medium held on for so long at the end came as a surprise.
"But hindsight is the thing. If we were to restart the race, maybe we would choose a different tyre."
Wolff said Mercedes could have decided to "lose more time on the medium and hang it out there for another five or six laps, and then try to do 30 laps on the soft" like Ricciardo did, but he felt it was "not a given that it would hold on" to the end of the race.
Both Hamilton and Russell's race engineers were heard during the race telling their drivers that the Red Bulls' mediums were expected to drop off in pace, only for them to last longer than expected and for them to finish behind Verstappen and Perez.
Wolff said Mercedes had discussed using on softs in the race and felt the tyre was "strong", but "not strong enough to go 30 laps or so."
Asked by Motorsport.com if he thought the medium-soft strategy would have been enough to beat Red Bull today, Wolff replied: "I don't think we could have overtaken them, because [with] the gaps, that would have been basically the reverse strategy.
"Even the soft-medium, that would have been a bit of an advantage into Turn 1. Lewis was on the outside, so you never know how it would have come.
"But we would have been even closer on a different strategy."
Mercedes comfortably ran as the second-fastest team ahead of Ferrari in Mexico, aided by the high altitude that meant it did not struggle with drag as much as at other tracks, as well as benefitting from its high downforce strength.
The team now has just two more chances to end its winless campaign, but Wolff said the simulations suggested Mexico had been its best chance.
"On the simulations, it says yes," he said. "But we see the tendency, we see that we are able to compete.
"I'm really proud of the team of what we did this weekend. We experimented with a lot of things, the engine guys have pushed the boundaries really to give us the maximum performance also.
"I think it will be a mix between trying the max while trying the most for next year."
