Ferrer, who is trying to win on Mexican soil for the fourth time in his career, defeated Kukushkin 6-2, 6-3 and will play Spanish compatriot Feliciano Lopez in the round of 16.
"I*m not thinking about the final, I'm only in the second round", Ferrer said. "Now I'm only thinking about playing my best tennis against Feliciano Lopez, he's a good player I need to give my best to beat him".
Ferrer, who now has a 4-0 record against Kukushkin, is coming off an impressive run in the past two weeks of the ATP tour, winning the Buenos Aires tournament and reaching the semi-finals in Rio de Janeiro last week.
"Playing in Buenos Aires was not in my plans", said Ferrer who replaced his countryman Rafael Nadal in Argentina. "I'm tired, but I will not be making any excuses, I need to take a rest now and get well for the rest of the tournament".
Karlovic served 15 aces to Isner fired eight in a match between two of the game's biggest servers.
"I'm very disappointed," a visibly upset Isner said after the match. "I wanted to do well in here, is a good surface for me, but I played against a guy who played well against me".
The 2.11m (6-foot-11) Karlovic now has a 3-2 career record against the 2.08m (6-foot-10) Isner, who's ranked 13th in the world.
Joao Sousa of Portugal came back to defeat Frenchman Adrian Mannarino 1-6, 6-2, 6-2 to advance to a second-round encounter against the winner of the later match between Andy Murray and Pablo Andujar.
South Africa's Kevin Anderson downed Stephane Robert of France 6-2, 7-6 (9/7) and will next play America's Sam Querrey. Also, Alexandr Dolgopolov, from the Ukraine, beat Canada's Vasek Pospisil 6-2, 6-2 and seventh-seeded Ernests Gulbis had a 6-1, 6-1 victory over Taiwan's Yen-Hsun Lu.
Latvia's Gulbis won his fifth career title last week in Marsella.
Results from day 2 of the Abierto Mexicano Telcel on Tuesday
David Ferrer (ESP x1) bt Mikhail Kukushkin (KAZ) 6-2, 6-3
Feliciano Lopez (ESP) bt Edouard Roger-Vasselin (FRA) 6-4, 6-2
Kevin Anderson (RSA x5) bt Stéphane Robert (FRA) 6-2, 7-6 (9/7)
Ivo Karlovic (CRO) bt John Isner (USA x3) 7-6 (7/4), 7-6 (7/5)
Oleksandr Dolgopolov Jr. (UKR) bt Vasek Pospisil (CAN x8) 6-2, 6-2
Ernests Gulbis (LAT x7) bt Lu Yen-Hsun (TPE) 6-1, 6-1
David Goffin (BEL) bt Lukasz Kubot (POL) 6-4, 2-6, 6-4
Marcos Baghdatis (CYP) bt Miguel Ángel Reyes (MEX) 6-2, 6-4
Grigor Dimitrov (BUL x4) bt Marinko Matosevic (AUS) 7-5, 6-1
Gilles Simon (FRA x6) bt Tim Smyczek (USA) 6-1, 6-2
Donald Young (USA) bt Jarkko Nieminen (FIN) 6-3, 6-3
João Sousa (POR) bt Adrian Mannarino (FRA) 1-6, 6-2, 6-2