"We have a discussion every night about Ichiro," Seattle manager John McLaren said, shaking his head about his seven-time All-Star. "I'm running out of superlatives."
Suzuki scored and drove in the other run for the Mariners, who have won four straight and moved within three of the division-leading Angels.
Los Angeles had won four in a row, including three impressive victories over defending AL champion Detroit. The Angels scored 34 runs against the Tigers, only the second time in their 47-year history that they scored at least 10 runs in three consecutive games.
They struggled against Batista (11-7), who struck out two and walked none in his first scoreless start this season. Brandon Morrow pitched a scoreless eighth and J.J. Putz needed just six pitches to complete the four-hitter and earn his 31st save in 32 chances.
Putz struck out Angels slugger Vladimir Guerrero on three pitches.
"Sometimes, things switch like that," said Los Angeles manager Mike Scioscia, whose team was shutout for the sixth time. "But overall right now I'd say we are in better shape than we were three weeks ago."
Suzuki led off the third inning by hitting a drive to the right-center field wall against Kelvim Escobar (11-5), who allowed eight hits in his third complete game this season. Suzuki then tested the vaunted throwing arm of right fielder Guerrero by speeding around second as Guerrero picked up the ball. He reached third easily as Guerrero's throw was wide of the base, and scored on Jose Vidro's single to make it 1-0.
"He is amazing," Escobar said. "You bounce the ball up there and he will still hit it. You go outside ... you go away ... He is just a great hitter."
Batista and Suzuki weren't downplaying the importance of Seattle's most important series in years.
"I don't think there's anybody on this team that doesn't feel that way," Suzuki said.
Batista added: "We know how important it is to put the pressure on now."
The 36-year-old Batista was sharp throughout, showing why the Mariners gave him a $25 million, three-year deal last winter and tying his career high for wins.
"Well, I have a team that can catch and hit for me," said Batista, who played for the Diamondbacks last season and has pitched for eight teams in his career. "Last year, I had 14 no-decisions."
He had some luck Monday. After Reggie Willits singled and stole his 22nd base with two outs in the fifth, Chone Figgins backed away from a 2-2 pitch that appeared to be off the inside edge of the plate. Umpire Derryl Cousins called strike three to end the inning. Figgins looked at Cousins in disbelief before telling him forcefully "That pitch was a ball."
Figgins also struck out against Batista in the third, the middle man in a three-batter escape. Jeff Mathis and Willits singled to begin the inning before Batista struck out Figgins on a 91 mph fastball and got Orlando Cabrera to foul out.
Then Guerrero, 12-for-21 in his career against Batista at that point, hit a sinking liner. Hobbled left fielder Raul Ibanez caught the ball inches above the grass while tumbling to end the inning and save at least one run.
Almost everyone in the Mariners dugout had high-fives and back slaps waiting for the 35-year-old Ibanez.
- Morrow was in the setup role now that RHP Chris Reitsma says he's out for the season as he prepares for the fifth elbow surgery of his career Thursday.
- Figgins was 0-for-3 with a walk after going 11-for-17 in his previous four games.