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 Brewers: Brewers left-hander Chris Narveson will cross another threshold in his comeback on Wednesday with a start against the Royals at Surprise Stadium, his first outing since undergoing shoulder surgery last May. Narveson is scheduled for about two innings, manager Ron Roenicke said, in a game available via webcast at Brewers.com beginning at 2 p.m. CT. Right-hander Luke Hochevar starts for Ned Yost's Royals.
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.