GLENDALE, Ariz. -- Carson Palmer threw for three touchdowns, moving ahead of Joe Montana on the NFL's all-time passing yards list in the process, and the Arizona Cardinals forced Jameis Winston into five turnovers Sunday on their way to a 40-7 rout of the Tampa Bay Buccaneers at University of Phoenix Stadium.

Coach Bruce Arians had said teams with good character "never lose two games in a row," and it became pretty clear during the second quarter when Arizona scored 24 points that there wasn't about to be a repeat performance of last week's 23-21 loss to the New England Patriots.

Unlike that game, the Cardinals (1-1) were able to uncork the big plays on offense that made them so dangerous a year ago. They also did a far superior job of tackling and pressuring on defense.

"We obviously are very pleased with the win," Arians said. "I thought our guys had a heck of a week of practice and it showed up on the field. ... I'm really happy to be 1-1."

Though they only sacked Winston twice, they recovered a fumble he lost and intercepted him four times. Marcus Cooper had two of the interceptions, including a pick-six he returned 60 yards for a third-quarter touchdown.

Palmer, meanwhile, threw touchdown passes to Larry Fitzgerald, Michael Floyd and Jaron Brown. Palmer entered the game needing 245 yards to move past Montana (40,551) for 16th place on the league's all-time passing yards list. He finished with 308 yards on 18 of 31 passing.

Winston, who threw for four touchdowns in a win last week over the Atlanta Falcons, was 27 of 52 for 243 yards and one score, a 19-yard strike to Mike Evans. His 52 pass attempts were a career high.

Buccaneers coach Dirk Koetter was asked about Winston staying in the game for its duration, even though this one was over early.

"I don't think Jameis would have come out," he said. "He struggled. A lot of guys were finishing the game for both teams. We could have taken him out but he wanted to finish. Some of you may not understand this, but the captain always wants to go down with the ship and that's how it is and Jameis is that kind of guy."

Cardinals running back David Johnson had 143 total yards from scrimmage, rushing 12 times for 45 yards and catching three passes for 98 more. In seven career starts dating back to Week 13 of last season, Johnson has 933 yards from scrimmage -- the most in the NFL.

The Buccaneers (1-1) lost a few players to injury, including starting running back Doug Martin, who left in the second quarter due to a pulled hamstring. He had seven carries for 23 yards before exiting for good.

Asked how Martin's absence affected the game, Koetter said, "It takes out one of the best running backs in the league. ... No one feels sorry for you, but you've got to keep playing."

Fitzgerald caught six passes for 81 yards and now has three touchdown receptions through two games. Evans finished with six catches for 70 yards.

The Cardinals converted two of the three turnovers they forced in the first half into 10 points on their way to taking a 24-0 lead at the break.

Arizona opened the scoring by driving 67 yards on 11 plays, capped by a 4-yard scoring pass from Palmer to Fitzgerald on the second play of the second quarter.

The Buccaneers turned it right back over to the Cardinals when Winston was intercepted for a second time. Cooper, a late trade acquisition, did the honors when he outfought Vincent Jackson for the ball, helping to set up a 22-yard field goal by Chandler Catanzaro.

Cooper, who was splitting reps early at right corner along with rookie Brandon Williams, is now up for the starting job by his lonesome.

"I don't know," he said. "Brandon is a good cornerback. He is still young but he's learning and we are going to continue to progress and whatever coach needs me to do ... I am just here to do."

Winston lost a fumble late in the second quarter. Tony Jefferson recovered for the Cardinals, and after a 27-yard completion from Palmer to Brown and a 24-yarder to Fitzgerald, Floyd hauled in a 1-yard touchdown as the Cardinals widened their lead to 17-0 with 1:30 left in the half.

Winston couldn't get anything ignited and the Bucs had to punt. Arians chose not to run out the clock, however. He went for the throat and after three plays, Palmer threw a deep ball down the middle to Brown, who took it into the end zone for a 51-yard score.

"When you play against a high-powered offense like Arizona, you can't give them freebies," Winston said of his five turnovers. "... All those interceptions were on me."

NOTES: Rookie DT Robert Nkemdiche was inactive for the Cardinals after being a late addition to the injury report on Friday with an ankle issue. ... Buccaneers TE Luke Stocker left the game in the first quarter with an ankle injury and did not return. ... Tampa Bay WR Cecil Shorts exited in the third with a pulled hamstring. ... With his second-quarter touchdown reception, Cardinals WR Larry Fitzgerald surpassed Hall of Famers Tim Brown and Steve Largent for sole possessions of eighth place on the NFL's all-time list (101).