Mercedes faced serious challenges during the day, with George Russell crashing out of FP2 after spinning out of control and colliding with the barriers.
Red Bull also had their own issues as Max Verstappen's run time was severely limited due to ongoing issues with the RB20.
FIA issue bizarre F1 penalty in Mexico
Oliver Bearman and Alex Albon also found themselves in the mix of things, with the Williams star losing control of his FW46 as he encountered the Ferrari heading through Turn 9.
Albon spun into the barriers prompting the yellow flags to be brought out, something which caught out Robert Shwartzman, deputising for Zhou Guanyu in FP1.
The Ferrari academy driver was hit with a five-place grid penalty for overtaking Yuki Tsunoda under the yellow flags that were brought out as a result of Albon's crash – but the F1 rookie is not due to take part in Sunday's race.
The decision states that the penalty will apply "for the next race in which the driver participates," meaning that Shwartzman may never serve his penalty.
A statement from the FIA read: "The penalty is the usual penalty for passing under a double yellow, and while the Stewards recognise that the driver is not scheduled to start the race, they have applied the consistent penalty."
Zhou will therefore not be impacted by the penalty and will hope to qualify as far up the grid as possible in a bid to score Sauber's first points of the F1 season.
His team-mate, Valtteri Bottas, has a 100% record of making it into Q3 at the Mexican Grand Prix, an achievement he will be desperate to keep this weekend.