Fitzgerald finished with five catches for 52 yards and Palmer completed 26-of-37 passes for 314 yards as the Cardinals (7-4) extended their rebound from a 3-4 start.
Michael Floyd made seven receptions for 104 yards.
Cardinals Coach Bruce Arians posted a win in his first game against Indianapolis since guiding the Colts to a 9-3 record as interim coach for leukemia-stricken Chuck Pagano last season.
After winning Coach of the Year honors, he signed a four-year deal with Arizona in January.
The AFC South-leading Colts (7-4) were paced by Andrew Luck, who went 20-of-39 for 163 passing yards, a touchdown and an interception.