The former Barcelona midfielder saw his stunning first-half strike cancelled out by Oscar de Marcos but struck again after the interval to take his season tally to three.
Sergio Garcia's goal sealed the points despite Ibai Gomez's late free-kick for the visitors as Espanyol moved up to fifth, level on points with fourth-placed Villarreal, and extended their unbeaten start to five matches.
Sanchez's 20-yard effort illuminated a hard-fought first half as the 26-year-old netted just his sixth goal in the Spanish top flight after 24 minutes.
Having raced from a central position to near the corner of the 18-yard box, he showed exceptional balance and composure to connect beautifully with a left-footed shot that flew past Gorka Iraizoz.
Javier Aguirre's side looked relatively comfortable with their one-goal advantage but saw it disappear a minute before the interval after good work from Benat provided De Marcos with the equaliser.
The hosts were not to be denied, however, and Sanchez scored again just two minutes after half-time, steering home Garcia's cross from inside the box.
Garcia got in on the act himself with a close-range header after Iraizoz had initially denied him and Christian Stuani in the 66th minute, ensuring that Gomez's last-minute set-piece effort was merely a consolation.
