Heilman was born in Logansport, Indiana and attended Logansport High School, where he was a letterman in baseball. As a senior, he was a team M.V.P. and an All-State selection. Heilman graduated from Logansport High School in 1997.
Heilman was selected by the Mets in the first round of the 2001 Major League Baseball Draft. He signed and made his professional debut that year with the Class-A Advanced St. Lucie Mets. He pitched for the Double-A Binghamton Mets and Triple-ANorfolk Tides in 2002, and began the 2003 season with the Tides. Heilman made his major league debut at Shea Stadium on June 26, 2003 in a 6-1 loss to the Florida Marlins. He posted an earned run average of 5.93 as a starter for 2003, 2004 and the beginning of 2005. Heilman's finest game came as a starter on April 15, 2005, when he made a start in place of the injured Kris Benson and pitched a one-hit complete game shutout. However, he was converted to a relief pitcher for the rest of 2005 and excelled with an ERA of only 2.18. In the second half of the 2005 season, he held a 0.68 ERA, leading the league. In Game 7 of the 2006 National League Championship Series, Heilman surrendered a tie-breaking, two-run home run in the top of the ninth inning to Yadier Molina of the St. Louis Cardinals, putting St. Louis ahead 3-1. St. Louis would hold on to the lead to win the National League pennant, while Heilman suffered the loss for the Mets.
On November 19, 2009 Heilman was acquired by the Diamondbacks, in return for Scott Maine and Ryne White. He elected free agency on November 7, 2010. He re-signed with them on January 18, 2011. He was expected to compete for a spot in the starting rotation. He was released on July 19, 2011.
The Phillies signed a minor league contract with Heilman on July 22, 2011. He was assigned to the Triple-A Lehigh Valley IronPigs. He was released on August 20, 2011.
Heilman signed a minor league contract with the Pittsburgh Pirates on August 21, 2011, and was assigned to the Triple-A Indianapolis Indians. He elected free agency on November 2, 2011.
Seattle Mariners
Heilman signed a minor league contract with the Seattle Mariners on January 10, 2012, with an invite to Spring Training. He was released on April 1.
Heilman signed a minor league deal with the Texas Rangers on April 4, 2012 and was assigned to the Triple-A Round Rock Express. He elected free agency on November 2, 2012.