The 22-year-old Walker, looking to lock up a rotation spot, struck out six and walked one in six more shutout innings. He gave up two hits.
"I feel like each start, everything starts to get better," Walker said. "My fastball location gets better each start, my off-speed does, too. I'm just trying to go out there and attack."
Mariners manager Lloyd McClendon stopped short of putting Walker in the regular-season rotation, though.
"Stay consistent," McClendon said. "He threw up a lot of zeros and he pitched well."
Zunino launched his team-leading fourth home run and Robinson Cano had two hits for Seattle, including an RBI double.
"It's coming along. It's feeling better. Recognizing pitches, more balanced and it's nice to have these couple of at-bats and these hits to build on that," Zunino said.
Chicago left-hander Travis Wood, also competing for a starting job, allowed three runs and five hits in five innings. He struck out three and walked two.
Walker, who has made 11 major league starts, put two runners on in the sixth but escaped by getting Dexter Fowler to bounce into a double play.
Mariners closer Fernando Rodney struck out two in one inning and is unscored upon in six spring innings.
Cubs shortstop Starlin Castro returned after missing the past few days with tightness in his groin and appeared to be moving well. He looked fairly smooth scooping up the three grounders hit to him and he hustled up the first base line on an infield hit and groundout.
Cubs: LHP Jon Lester has been dealing with a "dead arm," but will pitch in a minor league game Thursday. He's made three previous spring training starts.
Mariners: C Jesus Sucre returned after missing the past few days with a sore hip. He was a mid-game replacement for Zunino.
Wood batted eighth for the first time. He hit .232 with three home runs and 10 RBIs last season, making him a bench option in an emergency.
"Whenever my spot comes up I'm ready," he said.
As for his performance on the mound, Wood said he located well and his cutter was effective.
"I'm ready," he said. "It's late in the spring. ... Hopefully I get the last couple (outings) out of the way, and be ready to go."
McClendon said OF Dustin Ackley will bat at the bottom of the order this season, after acknowledging a mistake to put him near the top for part of last season. "To hit at the top of the order it takes a different mindset, and in some ways it probably messed with his psyche a little bit," McClendon said. "I was just trying to find a spark."
Cubs: LHP Eric Jokisch makes his fourth appearance and second start of the spring Thursday against the Angels.
Mariners: Felix Hernandez faces the Royals on Thursday after giving up six runs over 2 2-3 innings in his most recent outing. Hernandez has been limited this spring to manage his workload before the regular season.
All content copyright ©2015 Daily Journal, a division of Home News Enterprises unless otherwise noted.