The Rams, ranked 27th in offense, came out throwing, with Bradford completing passes of 14 yards to Brandon Gibson and 44 yards to Amendola on the first two plays, setting up the score to Kendricks on third down. It was the first offensive touchdown in three games for St. Louis.
Arizona responded with a drive that lasted 9:24, ending with Jay Feely's 35-yard field goal. The Cardinals kept the drive alive with three third-down conversions. Larry Fitzgerald's 5-yard catch on the first play of the drive marked the 122nd straight game with a catch, a franchise record.
Zuerlein, a sixth-round draft pick out of Missouri Western, made it 10-3 early in the second quarter. He is 13 for 13 this season, including four kicks of 50-plus yards.
Feely missed a 40-yard field goal late in the second quarter.
Bradford was 3 for 4 for 65 yards on the opening drive before cooling off. St. Louis was well within Zuerlein's range at the Arizona 16 late in the third quarter when a pass was intercepted by Patrick Peterson in the back of the end zone.
The Cardinals were still the St. Louis Cardinals the last time they were 4-0, in 1974. Known as the "Big Red," those Cardinals won their first seven that season en route to a 10-4 record, before losing in the first round of the playoffs to Minnesota.
The loss was only the Cardinals' third in 14 games since starting the 2011 season 1-6.