The Mariners chased Leiter after only two innings in building a huge lead, letting Garcia coast to a 13-1 victory over the New York Mets in the first game of a doubleheader Sunday.
"It's lucky when they score a lot of runs for you," Garcia said.
Suzuki singled four times as the Mariners matched a team record with their 10th win on a road trip. They improved to 16-0 in day games this season, and the outcome was never in doubt as Seattle took a 12-0 lead in the fourth inning.
"It just started off a bad day and it just stayed that way,'' Mets manager Art Howe said.
Garcia (6-6) pitched a six-hitter in his first complete game since May 19, 2002. He struck out seven and walked one.
Garcia joined the hit parade, too, with an RBI single in the first.
"I like to hit, but it's pretty hard,'' he said.
Suzuki led off the game with a single, stole two bases and scored as Seattle rushed to 4-0 lead in the first inning. Suzuki singled to start the second inning and scored again as the Mariners made it 8-0 against Leiter.
Leiter (6-3) allowed nine hits and three walks. It tied his shortest outing ever in the regular season for the Mets -- in the 1999 NLCS against Atlanta, however, he was chased before recording a single out.
"Any time you give a good pitcher that kind of a lead, it just makes his job that much easier and our guys' job that much harder,'' Leiter said.
Suzuki hustled for an infield single in the ninth that drove in a run. The two-out single was the Mariners' 17th and final hit.
"He likes his hits and I don't blame him,'' Mariners manager Bob Melvin said. ``Over the years, obviously, he's got a lot of them.''
Cliff Floyd hit his 12th homer in the fourth for the Mets' run.
Randy Winn got his second hit of the game, an RBI double with two outs in the second. That made it 6-0, and Leiter then threw consecutive wild pitches that each scored a run.
Cameron and Ben Davis had two-run singles in fourth off Jeremy Griffiths, who made his second major league appearance.
Seattle improved to 10-1 on its trip to Kansas City, Minnesota, Philadelphia and Shea Stadium. The Mariners' best swing ever was 10-0 in April 2002.
The Mariners have scored 61 first-inning runs in 60 games this season. ... Mets LHP Mike Stanton pitched a perfect eighth in his first appearance since May 21. He'd been on the disabled list because of an inflamed left knee. ... Garcia's single made him 7-for-21 as a major league hitter. He made outs in his next four at-bats. "I know my numbers,'' Garcia said with a grin. ... Leiter lasted two innings last Sept. 1 against Philadelphia. ... This doubleheader was caused by a rainout Saturday. The Mets have played two previous doubleheaders this season and been swept at home both times -- on Thursday against Milwaukee and on April 27 against Arizona.