The 22-year-old right-hander did not allow a hit until Zach Lutz singled with two outs in the fourth inning. Hector Pellot got the Mets' only other hit off Drabek, leading off the sixth with a single.
Drabek followed Pellot's base hit by striking out Kirk Nieuwenhuis and Nick Evans. But he walked Lucas Duda and Lutz to load the bases and was relieved by Adrian Martin.
MLB.com's No. 17 prospect, Drabek (3-1) lowered his ERA to 3.80 as he became the Eastern League's third three-game winner. The Blue Jays acquired him from the Phillies last December as part of the blockbuster deal involving Roy Halladay.
Drabek, the son of former Cy Young Award winner Doug Drabek, received the 2009 Paul Owens Award as the top pitcher in the Phillies Minor League system. He was 4-1 with a 2.48 ERA in 10 games at Class A Advanced Clearwater, earning Florida State League All-Star status before a promotion to Double-A Reading, where he went 8-2 with a 3.64 ERA in 15 games.
Drabek's effort overshadowed the 2010 debut of Binghamton starter Brad Holt, who missed the first two weeks of the season due to a wrist injury. The former first-round pick took the loss after giving up a run on three hits in two innings. He walked a batter and struck out two.