Cardinals quarterback Carson Palmer spikes the ball after his 8-yard touchdown run for the game-winning points in Sunday's 19-13 win over the 49ers.

SANTA CLARA, Calif. – No apologies were coming out of the Cardinals' locker room Sunday afternoon, and there wasn't any anger.

It had, as coach Bruce Arians said, "nothing to do with traps and all that (expletive)." Their view of their admittedly ugly 19-13 win over the last-place 49ers at Levi's Stadium was simply that – it was a win, on the road and within the division, and that was all that mattered.

"It was hard sledding," Arians said. "It was not sexy whatsoever."

If the Cardinals (9-2) want to return here in February to play in Super Bowl 50, they will have to play better than they did against the 49ers (3-8). Much better. They have to hope that none of the injuries that came out of the game are serious,

after starting cornerback Jerraud Powers (likely a calf, but possibly an Achilles) and running backs Chris Johnson (left knee) and Andre Ellington (right foot) all had to depart.

But after quarterback Carson Palmer capped a 14-play drive with an eight-yard touchdown scramble for the game-winning points and the defense held up on the 49ers' final possession, the Cardinals winning streak – now at five games – is intact, as is their three-game lead in the NFC West. It was the Cards' first win at San Francisco since 2008, breaking a six-game losing streak.

"It's a division game on the road," defensive tackle Calais Campbell said. "No one expected it to be easy."

Easy, perhaps not. Easier, though, after the Cardinals had put up 39 and 34 points on the top two scoring defenses in the league the previous two weeks and after blowing out the Niners, 47-7, earlier this season.

The Cardinals won the turnover battle for the first time in more than a month, but the lack of a run game – a mere 70 yards – and an inability to put the ball in the end zone left the score tied at 13 in the fourth quarter.

The odd game featured 26 first downs by the Cards and a huge time-of-possession advantage (37 minutes to 22) but the

Cardinals had fewer yards than the Niners.

"They've had a tough season but they came to fight," Palmer said. "That's what we're going to get being on top the way we are. We're going to get everybody's best shot because people want to knock us off."

The game-winning drive was helped with one of the 13 penalties against the 49ers, a crucial roughing-the-passer call after a Quinton Dial sack of Palmer.

"He hit me right in the face with the crown of the helmet," Palmer said.

The Niners sacked Palmer later in the drive to put the Cards into a second-and-14 situation on the San Francisco 35-yard line, when Palmer let loose possibly his best pass of the day – a chuck off his back foot that found an open J.J. Nelson downfield for a 34-yard gain.

Nelson said the call was similar to the one the week before against the Bengals in which Palmer hit him for a 64-yard TD.

"I knew if I got behind the second level, Carson was going to be able to get me the ball," Nelson said.

On this day, it wasn't going to be simple, though. There would be no one-yard TD run; instead, after a two-yard running loss and a penalty, Palmer scrambled as fast as he could to the left pylon to score with just 2:38 left. The built-up emotion led to a resounding Palmer spike afterward, and Palmer fell as he followed through.

"I thought he threw his back out," cornerback Patrick Peterson said with a smile.

In keeping with the theme, though, kicker Chandler Catanzaro missed the extra point, and the Cardinals were forced to get a stop on an afternoon when Niners quarterback Blaine Gabbert actually had more passing yards than Palmer (318 to 271).

"As a defense, if we want to be where we want to be at the end of the year, we can't keep having these roller-coaster rides," Peterson said.

The 49ers reached the Arizona 30, but on third-and-10, the Cardinals brought a full blitz, and safety Tony Jefferson – liked he sacked 49ers quarterback Colin Kaepernick on a key play in Arizona in 2014 – again got home.

"Déjà vu from last year," Jefferson said.

The play cost the 49ers 10 yards, and Gabbert's fourth-and-20 pass covered 18 yards to Anquan Boldin, essentially ending the game.

The Cardinals will go through the same scenario in a week, when the Cardinals play a struggling (4-7) NFC West team (the Rams) on the road (St. Louis). That, at least, has a revenge factor after the Rams beat the Cards in Arizona earlier this season.

Arians had a small smile after the game, proclaiming the ability of his team to learn a lot from Sunday. His own takeaway?

"We are good enough to win without our best," Arians said.