The Brewers got one run back in the bottom of the inning on a Blake Lalli solo homer, but the Mariners held on and improved to 4-1 in the Cactus League. The Brewers are 1-4.
Smoak's homer was the game-winner, but Gutierrez's was the big blast. He is known more for Gold Glove-caliber defense than power, but batting against Brewers starter Yovani Gallardo in the third inning, he connected for a towering fly ball that cleared the center field batter's eye, a rare feat at Maryvale even in batting practice.
"You don't see many," Brewers left fielder Ryan Braun said.
Perhaps Gallardo is just getting the home runs out of the way.
"I hope so," he said. "Just pitches up, falling behind hitters in that third inning. I might have been starting to get a little tired. But I was able to get all of my pitches in, and that's the most important thing."
Marco Estrada, who will join Gallardo in Team Mexico's pitching rotation for the upcoming World Baseball Classic, fared much better, allowing only one hit over three scoreless innings. Estrada recorded all four of his strikeouts within a span of five batters and was the pitcher of record after the Brewers took a 4-3 lead on Kameron Loe's wild pitch in the fourth inning.
Mariners starter Hisashi Iwakuma pitched a scoreless inning in his first spring start, before Joe Saunders allowed three Brewers doubles and two runs in the second inning. Iwakuma is starting his second season with the Mariners after coming over from Japan last year.
"Last year I was more nervous and hesitant," Iwakuma said through translator Antony Suzuki. "This year I'm more relaxed and comfortable with one year under my belt. So it was a lot easier for me to adjust to getting back into the game."
Up next for Mariners: Top left-handed pitching prospect Danny Hultzen makes his first Cactus League start Wednesday, as the Mariners travel to Goodyear to face the Indians at 1:05 p.m. MT (12:05 p.m. PT). Hultzen zipped through one perfect inning of relief on just seven pitches -- all strikes -- Saturday against the Padres. Right-hander Taijuan Walker, the club's other premier prospect, will follow Hultzen, as both are scheduled to throw two innings. Also scheduled to pitch are Charlie Furbush, Hector Noesi, Lucas Luetge, Stephen Pryor and Josh Kinney.
Adam McCalvy is a reporter for MLB.com. Read his blog, Brew Beat, and follow him on Twitter at @AdamMcCalvy. This story was not subject to the approval of Major League Baseball or its clubs.