Gurley posted his third career game with at least three rushing touchdowns. He scored on runs of 11 and 19 yards, respectively, in the second quarter when the Rams built a 19-0 lead.
"We responded the right way physically and mentally [after a 33-13 victory over Oakland on Monday]," Gurley said.
Gurley also scored on a 2-yard run late in the third quarter and on a pair of two-point conversions.
Gurley only finished with 42 yards on 19 carries as he exited the game after the third quarter with cramps.
His three touchdowns helped the Rams get off to a 2-0 start for the first time since the 2001 season when the "Greatest Show on Turf" won its first six games before getting upset 20-17 by the New England Patriots in the Super Bowl.
"It feels good," Gurley said. "That just tells you how hard it is to win in this league, no matter what team you're playing against. Obviously, the first couple of weeks, you're still getting adjusted to the regular-season tempo. But it's these games that you need to win, so you won't have to catch back up in November and December. We just have to keep finishing these games and just take them week by week."
The fourth-year running back added three catches for 31 yards and moved up the Rams' rushing yards list. He now ranks seventh in franchise history with 3,446 after passing Les Josephson. Gurley trails Dan Towler by 47 yards for sixth.
Jared Goff produced an efficient performance by completing 24-of-32 passes for 354 yards, one touchdown for a 108.1 passer rating. It was his third triple-digit passer rating of his career and he finished one yard shy of his career high with his seventh game with at least 300 passing yards.
The Cardinals were dominated so much that they did not cross midfield until late in the third quarter. They mustered five first downs and dropped to 0-2 for the first time since 2005.
"You have to evaluate with everything," Wilks said. "I think when you look at the situation in all three phases that's what we're going to do. I'm not going to sit here and jump to conclusions right now, right after the game. We are going to go back and evaluate the film."
Arizona was also blanked for the second straight season by the Rams. Last season, the Cardinals absorbed a 33-0 beating when the teams met in London.
Larry Fitzgerald finished with three catches for 28 yards before exiting with a hamstring injury.
Arizona was outgained 432-137 and fell apart after a scoreless first quarter.
"When you look at the game, it's a little deja vu from last week," Wilks said. "We just couldn't find ourselves making a play."
The Rams took the lead early in the second quarter on Gurley's first score and two-point conversion.
Punter Johnny Hekker extended the lead with an 11-0 lead midway through the second quarter. He served as the kicker after starter Greg Zuerlein sat out with a groin injury after getting hurt in warmups.
Gurley scored on the final play before halftime and made it 27-0 with his third score. The Rams capped the scoring when Tyler Higbee hauled in a 3-yard pass with about three minutes left in the game.