Hudson picked up his 15th win of the season Thursday at Busch Stadium in St. Louis.
"I felt like it was a back-and-forth game," Hudson told reporters. "I felt like [I wanted to] get momentum on our side after our hitters have been hitting well. They kinda just continued that. I just tried my best to shut them down and allowed [our hitters] to keep doing their thing."
The Cardinals drew first blood with a Paul Goldschmidt RBI single in the first frame. Paul DeJong added a two-run homer in the same inning, before the Cardinals plated five more runs in the third inning. Rangel Ravelo hit his first career home run in the eighth inning for the final run of the game.
Giants starter Logan Webb allowed eight hits and eight runs in 2.2 innings. Webb is now 1-1 this season.
Goldschmidt went 2-for-3 with two runs scored, an RBI and a walk in the win. Matt Carpenter also went 2-for-3 in the win. DeJong, Ravelo and Hudson recorded two RBIs apiece for the Cardinals.
"Dakota did a nice job," Cardinals manager Mike Shildt said. "Obviously six shutout innings and was in control. He did a nice job of pitching with the lead, which we staked him to in the first. A lot of quality pitches and good stuff. It was another nice, really quality outing from Dakota."
The Cardinals start a three-game series against the Pittsburgh Pirates at 7:05 p.m. EDT Friday at PNC Park in Pittsburgh. The Giants battle the Los Angeles Dodgers at 10:10 p.m. EDT Friday at Dodger Stadium in Los Angeles.