Ramirez, who has a 0.96 ERA this spring, struck out four without allowing a walk. He hit one batter with a pitch.
"I was lucky sometimes because I missed the spot ... and was right in the middle of the strike zone," Ramirez said.
Mariners manager Lloyd McClendon thought Ramirez was "OK."
"We have to make better 0-2 and 1-2 pitches," McClendon said. "He got some balls up in the zone that he got away with. On any given day, you don't get away with those pitches. Even in wins, there are things you need to correct, that we need to talk about.
"But for the most part, he threw the ball OK."
McClendon stopped short of announcing that Ramirez has won a spot in the rotation.
"I'm not ready to answer any of those things yet," he said.
Cano was 2 for 3 to raise his batting average to .567. Dustin Ackley went 3 for 4, lifting his average to .457.
Mariners pitchers limited the Cubs to four hits. Joe Beimel, Fernando Rodney and Yoervis Medina each pitched a scoreless inning.
Jeff Samardzija, in his next-to-last spring outing before his opening-day start for the Cubs, gave up two runs and six hits in 5 1-3 innings. He struck out eight and walked two.
Another Cactus League attendance record was set at Cubs Park with an overflow crowd of 15,191. The new stadium has drawn the eight biggest crowds in Cactus League history since the opener on Feb. 27.
Cubs: Samardzija gave up a run in the fifth, then wobbled in the sixth. He allowed a line-drive leadoff single by Corey Hart, then Logan Morrison drove a shot to the left field fence, where Junior Lake leaped up and made a homer-saving catch.
At that point, Samardzija was relieved by James Russell, who allowed Hart to score but, thanks to a great play in the hole at shortstop by Donnie Murphy, prevented further damage.
"I felt good today," said Samardzija, who said he worked on small mechanical changes to prevent him from leaving the ball too high in the strike zone. "The ball was down in the zone. That was a problem over in Surprise" in his previous start.
Mariners: Projected starter Taijuan Walker threw a bullpen session Wednesday as he comes back from a sore shoulder.
Cubs: Shortstop Starlin Castro, who has been dealing with a hamstring problem, is nearing 100 percent and could be playing in games within a few days.
Mike Olt, who has been dealing with shoulder soreness while enjoying a fine spring at the plate, played third base for the first time. He had been used as a designated hitter.
Mariners ace Felix Hernandez threw 83 pitches over seven innings in a minor league game at the team's complex in Peoria.
"I hear he threw the ball pretty good," McClendon said.
Mariners: Cano has hit safely in eight straight games and 10 of 11 in Cactus League play. Overall, the Mariners' new second baseman is 17 for 30 with eight RBIs. He has two extra-base hits, both doubles.
Cubs: Javier Baez has five homers this spring, which was tied for most in the majors entering Thursday.