The young right-hander, who is 3-2 with a 4.19 ERA, has pitched better than his numbers suggest. Heilman has held opponents to three runs or less in four of six starts, including a one-hitter against Florida on April 15.
Heilman, 26, relieved for just the second time in his major league career, allowing one hit in 3 1-3 innings, striking out five to pick up a 7-5 win over the Philadelphia Phillies in his last appearance on Thursday.
“He’s probably been the most pleasant surprise,” Mets manager Willie Randolph said.
New York is out to a respectable 17-15 start under Randolph and has won six of its last eight games.
The Mets had their four-game winning streak snapped with a 5-4 loss to the Milwaukee Brewers on Sunday.
The Cubs had lost seven straight before Carlos Zambrano gave them a boost with a five-hit complete game shutout of the Philadelphia Phillies on Sunday.
Zambrano notched his fifth career complete game and first since May 7, 2004.
“It’s a tremendous relief,” Cubs manager Dusty Baker said.
Ryan Dempster was warming up in the ninth, a day after he was told he was becoming Chicago’s new closer. Dempster, 1-3 as a starter, was scheduled to start Monday against the Mets, but the Cubs told him of the switch Saturday. Dempster pitched in the bullpen late last season after returning from elbow surgery.
“It’s exciting,” Dempster said. “I don’t know what to say. Just go out there and when they call on me to do the job, try not to let anyone score.”
Baker has said the struggles of his closers have left him sleepless at night and said this move is definite until Joe Borowski returns from a rehab stint in Triple-A Iowa.
“Then we’ll make a decision,” he said.