The Lotus driver, who sits five points behind championship leader Isaakyan, traded places with the Russian throughout the 30-minute qualifying session at the Autodromo Hermanos Rodriguez.
Fittipaldi put a storming lap together with his final effort, a 1m31.382s, which put him 0.380s ahead of Teo Martin's Palou, who only got the call to travel to Mexico on Tuesday.
Palou's own last lap squeezed him above Isaakyan and out to the front row by 0.022s.
Just behind Isaakyan on the second-row for race will be Force India Formula 1 development driver Alfonso Celis.
The Fortec racer, competing in front of his home fans, set the pace early on in the session but could not find the half-a-second needed to try and unseat Fittipaldi.
Konstantin Tereschenko and Egor Orudzhev ended up fifth and sixth, with the latter saying he felt comfortable on the Mexico City track despite it lacking grip after repeated heavy rain showers throughout the week.
Diego Menchaca will start seventh, and Rene Binder lines up next to him.
Rounding out the 11-car grid are Roy Nissany, Yu Kanamaru and Giuseppe Cipriani, who qualified almost three-seconds behind first place.
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