Lewis Hamilton who could secure his sixth World Championship if things go his way on Sunday, struggled at first but was able to top the session ahead of Ferrari's Charles Leclerc.
The Brit, alongside his Mercedes teammate Valtteri Bottas, struggled with a tail-happy back-end and said, “The rear end is all over the place”, but the Silver Arrows still managed to get a car at the very front.
Ferrari failed to match Mercedes but their is the feeling that the red cars will have much more to offer going forward into the weekend.
Sebastian Vettel ended the session in sixth and became frustrated as he kept running into traffic, contributing to the distance to his teammate in second.
Having won the previous two Grand Prix in Mexico, you cannot write-off Red Bull this year, even with the straight-line speed deficit on their two rivals Ferrari and Mercedes.
Max Verstappen seems the more likely Red Bull driver to battle at the very front, with the Dutchman finishing in third place ahead of teammate Alexander Albon who edged ahead of both Bottas and Vettel.
Tricky Turn 1
The opening corner on the circuit proved challenging for drivers throughout the session with several cars carrying too much speed and drifting onto the grass run-off area.
Midway through the session Bottas locked his right-rear tyre as he approached Turn 1 and as a result was forced to run wide. Vettel also went very deep into Turn 1 and had to demonstrate how to safely re-join the track at Turn 3.
Alfa Romeo’s Antonio Giovinazzi struggled to get to grips with the track, with FP1 being his first session on the Mexican circuit in a Formula 1 car and the Italian was the latest to lock-up in the opening sequence of corners, but eventually hooked up a lap to earn a tenth place finish.
George Russell and Kevin Magnussen pushed too hard in the final moments and bailed out of their laps after drifting wide at the first corner.
Red flag for Stroll
Lance Stroll had been going well in eighth place but after losing the car in Turn 16, he collided with the barriers, but was able to get back on the track after repairs to finish 16th.
As the FIA stopped the session with 30-minutes of the session remaining, replays showed that Stroll lost the rear as he accelerated through the right-hander, with a sharp snap of oversteer resulting as the cause for the Racing Point to limp back to the pit-lane with a heavily damaged left side and a broken rear wing.
The other Racing Point of Sergio Perez had a tricky first session of his home race and the Mexican could only manage 17th.
Rest of the pack
The Toro Rosso's were closely matched in eighth and ninth, behind McLaren's Carlos Sainz who finished best of the rest whilst his teammate Lando Norris was off the pace in 14th.
After getting disqualified from the Japanese Grand Prix last time out, Renault will be looking to bounce back in Mexico and with Nico Hulkenberg finishing in 11th ahead of his teammate Daniel Ricciardo in 15th, they will be hoping for further improvement ahead of qualifying.
Haas continued to struggle after having a season of very few ups and many downs with both drivers struggling to get anything out of the car. Romain Grosjean has been knocked out in Q1 for the previous three seasons and in FP1 he could only manage 18th behind teammate Magnussen in 12th.
The Williams cars have become accustom to rounding out the rear of the field and FP1 was no different, but there was some reason for optimism with back-up driver Nicholas Latifi impressing in the absence of Robert Kubica who has struggled to match Russell throughout this season.