The Buccaneers (1-1) got the ball back and were driving again when defensive lineman Josh Mauro tipped Winston's pass. Cooper grabbed it and outran defenders down the sideline to make it 33-7.
NEW CORNERBACK?: Arians said the plan was for rookie Brandon Williams and Cooper to alternate series, but once Cooper was in, he stayed in.
"He got hot," Arians said. "You don't take hot hands out."
Now Cooper may have the job all to himself.
"We'll see how it goes," Arians said. "He could potentially be the starter over there."
QUICK STRIKE: The Buccaneers were on their best drive of the first half when running back Charles Sims III brushed against Winston and the ball popped loose. Tony Jefferson recovered for Arizona at the Cardinals 29.
After the fumble recovery, Palmer's 24-yard pass to Fitzgerald eventually put the ball at the Tampa Bay 1. On third down, Palmer hit Michael Floyd in the back of the end zone and it was 17-0 with 1:36 to go in the half.
A quick three-and-out by the Buccaneers gave the Cardinals the ball at their 26, plenty of time for a high-octane offense finally getting in gear.
Jaron Brown got behind the defense and gathered in a perfect pass from Palmer for a 51-yard touchdown with 20 seconds still remaining until halftime.
WINSTON PICKED: Peterson outmaneuvered Mike Evans on Winston's deep pass to the end zone and intercepted .
Cooper returned an interception 23 yards to the Tampa Bay 19, leading to an Arizona field goal.
The third pick was Cooper again, for a touchdown. Winston's fourth interception came on the game's last play.
DO-EVERYTHING JOHNSON: The Buccaneers held David Johnson to 45 yards rushing in 12 attempts, but he caught three passes for 98 yards. The longest came on a check-down from Palmer, a play that went for 58 yards.
"I don't think you can find a weakness in his game," Palmer said.
NO SUBSTITUTION: Koetter got irritated when reporters kept questioning him on why he left Winston in the game when the outcome long had been determined.
"You could criticize me all you want," Koetter said. "He stayed in. The decision is made. So write what you are going to write."
INJURIES: Injuries hit the Buccaneers hard.
First, they lost tight Luke Stocker (ankle) in the first quarter. And after a 1-yard gain on Tampa Bay's first play of the second quarter, standout RB Doug Martin left with a hamstring injury.
Defensive end Robert Ayers Jr. left with an ankle injury late in the second quarter. Finally, wide receiver Cecil Shorts III left with a hamstring injury in the third quarter.