Pennetta, from Italy, has reached the finals in the Mexican Open four times, and won in 2005.
"There are a lot of matches before the finals, it's one step at a time," Pennetta said after the match.
Pennetta dominated the second set, breaking Bychkova's serve three times.
American Jill Craybas easily defeated Paraguay's Rossana De Los Rios 6-2, 6-2, and Spain's Lourdes Dominguez Lino dispatched Japan's Rika Fujiwara 7-5, 6-3. German Julia Schruff held off Hungarian Greta Arn 6-2, 6-7 (6), 7-6 (5).
On the men's side, third-seeded Juan Monaco rallied to beat fellow Argentine Juan Pablo Brzezicki 6-3, 2-6, 6-3. Spain's Nicolas Almagro cruised past Jiri Vanek of the Czech Republic, 6-1, 6-2. Spain's
Albert Montanes upset seventh-seeded Igor Andreev of Russia 7-6 (4), 6-3.