The Cardinals entered this season advertised as having the best minor-league system in baseball with a talent pipeline years in the making that they planned to exploit for years to come. It took less than two months before they had to test it. Lefty John Gast became the latest rookie to arrive and provide as he pitched six solid innings in his major-league debut Tuesday and followed the offense to a 10-4 victory against the New York Mets at Busch Stadium. Gast became the first lefty to make his big-league debut for the Cardinals as a starter since Rick Ankiel in 1999 and the first to win his debut since Allen Watson in 1993. But he’s just the latest in a parade of pitching prospects who have sped to the aid of the Cardinals. Gast’s first career victory was the eighth win by a rookie for the Cardinals already this season. Nearly a third of the team’s 25 wins belong to pitchers who hadn’t reached the majors as of last August. Half of the current 12-man pitching staff was in the minors 12 months ago. Three rookies who weren’t on the Cardinals’ opening day roster this year pitched the first eight innings of Tuesday’s win. “I’ve never seen this,” veteran Carlos Beltran said. “Being able to replace a guy who throws hard with another guy who throws harder? Imagine that. You don’t see that a lot. … These guys, they just come in and they feel comfortable. They don’t look intimidated at all. They look like they belong here.” Beltran backed Gast (1-0) with four RBIs and three hits, including his 10th home run of the season. Jon Jay added a solo home run later in the game, his fourth of the season and his second since altering his swing at the plate. Leadoff hitter Matt Carpenter reached base four times, adding to a stretch of 18 times on base in his past 29 plate appearances. The Cardinals had three separate three-run rallies against the feckless Mets, including two against their starter, Dillon Gee (2-5). The win was the Cardinals’ 11th in their past 13 games, and it comes at the threshold of the club’s most inviting stretch of the season so far. Including this four-game series against the Mets and a West Coast jaunt to San Diego and Los Angeles next week, the Cardinals will play 13 consecutive games against clubs with a losing record. In succession, the Cardinals will face four of the five worst pitching staffs in the National League. The next eight games are against the three highest ERAs in the league. The Cardinals did what they could to help 14th-ranked New York (4.59 ERA) near the league-worst 4.60 ERA Milwaukee brought into Tuesday’s game. There’s still time. The Brewers visit Friday. A willingness to lean on the minor-league system became a need this past week, though the Cardinals have spent the season confronting sudden uncertainties with internal answers. Pete Kozma took over for injured Rafael Furcal at shortstop. Shelby Miller, today’s starter, won Chris Carpenter’s spot in the rotation. Both answers spent the majority of last season in the minors. Jason Motte is out for the season, but Edward Mujica is 10 for 10 in save opportunities. When Jay faltered at leadoff, Carpenter ascended. Seth Maness and Carlos Martinez, who combined for two innings of scoreless relief Tuesday, arrived when Marc Rzepczynski and Mitchell Boggs struggled into demotions. “The list goes on and on,” Maness said. For every problem, the Cardinals have had a promotion. “It shows me that the Cardinals are willing to put young guys out there,” Gast said. “Shows they’re willing to trust us.”