Orudzhev was the only other driver to set a time in the 1m30s bracket, and it looked like the SMP Racing driver had a chance of improving on his final run before a big slide entering the stadium section spoiled his lap.
The Russian driver therefore ended up 0.124s adrift of Fittipaldi's best time.
On the second row, Celis pleased the home fans that attended the Autodromo Hermanos Rodriguez with a third place start for Sunday's second race.
Behind him in fourth was Lotus' Rene Binder, who overcame the engine issues that blighted his first qualifying session to set a best time of 1m31.148s, which put him 0.513s slower than his team-mate.
Fifth and sixth went to Alex Palou and Diego Menchaca, as the pair were unable to match the pace of the cars ahead on a track that had benefitted from more rubber going down during the 90 minutes of running by the World Endurance Championship cars, which the V8 3.5 series is supporting in Mexico this weekend.
Matevos Isaakyan couldn't match the pace he showed in the first qualifying session and was more than one-second adrift of Fittipaldi's pole time, finishing in seventh place after having several off-track moments during the 30-minute session.
Joining him on the fourth row is Yu Kanamaru, who edged out Konstantin Tereshchenko for ninth by just 0.065s with just a few minutes of qualifying remaining.
Roy Nissany and Giuseppe Cipriani complete the grid.
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