He went right after the St. Louis Cardinals' star, who has hit five grand slams this year, making him settle for a sacrifice fly.
Then he struck out Matt Holliday to end the inning, setting the stage for Dan Uggla's go-ahead two-run homer in the top of the sixth in the Marlins' 2-1 victory on Tuesday night.
The 23-year-old rookie left-hander also outpitched 18-game winner Adam Wainwright, striking out a season-best nine in six innings.
"He may not even know who Cy Young is, and he may not even know who Matt Holliday and Albert Pujols are," manager Fredi Gonzalez said. "But I hope that builds confidence and he keeps going."
West (7-5) embraced the moment while helping to keep alive the Marlins' faint playoff hopes and sending the NL Central-leading Cardinals to their fourth loss in five games. Florida is 51/2 games behind wild card-leading Colorado, while the Cardinals' magic number remained at 10.
"Do I know who Cy Young is?" West said. "Yeah, I've heard of him. I had a blast."
Pujols is 9 for 14 with 30 RBIs with the bases loaded.
"I didn't even want to know at the time," he said. "Our game plan was to pitch him in. I got a slider in at his feet and he popped it up and that was huge."
Wainwright (18-8) allowed two runs in seven innings with eight strikeouts, missing a chance to become the majors' first 19-game winner. He was happy with the pitch to Uggla, a 1-1 curveball that was ankle-high when Uggla golfed it over the left-field wall.
"I don't think it was a sloppy pitch," Wainwright said. "I'll take my chances with that almost every time, but he's a great hitter and he made a good swing."
Wainwright had been 6-0 with a 1.99 ERA in seven starts since Aug. 8. He's allowed two or fewer earned runs in 15 of 16 starts, with the exception a six-run inning against the Pirates on Sept. 4 -- even though he ended up winning his 17th game.
"I had a stupid inning in Pittsburgh," Wainwright said. "Other than that I've felt pretty much the same every time I go out there."