Derek Anderson hung in the pocket despite taking a pounding from the St. Louis pass rush, going 22 for 41 for 297 yards in his first start as the replacement for the retired Kurt Warner. Steve Breaston caught seven passes for 132 yards and Tim Hightower and LaRod Stephens-Howling combined for 103 yards rushing for an offense without Beanie Wells (knee).
Bradford was 32 of 55 for 253 yards and three interceptions.
The Rams (0-1) displayed daring on Bradford's 1-yard touchdown pass to Laurent Robinson on the final play of the half to tie it at 10. A sellout crowd was roaring after the Rams took the lead on Josh Brown's chip-shot field goal midway through the third quarter, before St. Louis lost its 14th in a row at home.
The Rams have lost 15 straight to NFC West opponents and eight straight to the Cardinals.
The Cardinals, the two-time defending division champions, had to hold off two late Rams charges.
Kerry Rhodes' interception on fourth-and-10 from the Arizona 21 just after the two-minute warning appeared to be the clincher, but Hightower's fumble gave the Rams another chance that finally fizzled when Adrian Wilson intercepted Bradford's last-ditch throw from the Arizona 36 as time ran out.
That was the third big play by Wilson, who blocked a field goal and had an interception in the first quarter.
The Cardinals also got a break when Rams defensive lineman Clifton Ryan was heading toward the end zone after a fumble recovery, a score that would have put the Rams up 20-10. But Breaston chopped the ball free and Lyle Seldlein recovered in the end zone for a touchback.
Fitzgerald, coming off a fourth Pro Bowl season, was held in check by cornerback Ron Bartell much of the game and had only three receptions for 43 yards. He finally shook free on the touchdown grab with 6:13 to go.
Breaston's fourth career 100-yard game, and first since 2008, picked up the slack.
Mark Clayton, acquired from the Ravens on Monday, had a career-high 10 receptions for 119 yards for St. Louis.
Arizona had totaled 12 yards rushing before putting together a 76-yard drive, all five plays on rushes, to take a 10-3 lead in the second quarter. Stephens-Howling had two carries for 36 yards and Hightower had a 20-yard carry to the 1 before taking it in the next play.
Wilson's first career block thwarted the Rams after Hightower was stripped on a carry by Oshiomoghe Atogwe on Arizona's first drive. Bradley Fletcher returned the ball 43 yards to the Cardinals 32.
Wilson has 21½ career sacks, 7½ coming against the Rams. He has five career games with a sack and an interception, including two straight games against the Rams.
Arizona wide receiver Early Doucet injured his left groin in the first half and did not return.