Anthony Rizzo led off the bottom of the ninth with a single off Mets reliever Scott Rice (1-2). After New York third baseman David Wright was unable to turn a hard-hit grounder into a double play, Schierholtz pulled a liner into the right-field corner against the left-handed Rice to win it.
"I know I'm a better player than I showed the first few months. That wasn't me. I knew it was going to come around. It took longer than I hoped, obviously I still have a lot to do in the next four months, but I'm confident and that's all that matters," said Schierholtz, who was 3 for 4 to move his average up to .224 from .212.
Schierholtz hit .251 with home 21 homers last season for the Cubs.
The Mets squandered an opportunity in the third when they had bases loaded and failed to score.
"We gave this away," Wright said. "Obviously, not being able to get that lead runner in the ninth and then we had numerous chances to put that team away. We couldn't do it. Any time you put that many runners in scoring position and you only come away with one, that kind of gets the momentum back on their side and they were able to take advantage of it late."
Mets starter Zack Wheeler pitched 6 2/3 scoreless innings and was in line for the victory until Josh Edgin gave up a leadoff home run to Coghlan to tie the game and snap a 15 inning scoreless streak for Chicago. It was the left-hand hitting Coghlan's first homer against a lefty pitcher since 2010.
After only giving up one run in 6 1/3 innings to the Phillies on Thursday, Wheeler gave the Mets another strong outing. He had little trouble going against an overmatched Chicago offense. He allowed two hits, while striking out seven and only allowing two walks. The 24-year old right-hander did not allow a runner past first base.
"I thought he did a real good job. I thought his location was outstanding. He didn't have his best stuff, but he moved the ball around and I was very impressed with the way he pitched," said Mets manager Terry Collins.
The struggles continued for Rizzo against Wheeler, who was ejected after striking out in his first at-bat on Sunday. He struck out three times against Wheeler and dropped a routine pop up in the eighth.
Matt den Dekker led off the game with a single. He stole second and advanced to third on a wild pitch then scored on Granderson's sacrifice fly.
"In some big situations I was able to make a lot of big pitches, too, keep it to one run and obviously things kind of led to what happened in the ninth, which is pretty awesome," said Arrieta.
Arrieta allowed one run on seven hits in 4 2/3 innings. He struck out two and walked three.
Arrieta's night ended early with a high pitch count. Cubs manager Rick Renteria was forced to pull the 28-year old right-hander after he walked Duda with two outs in the fifth on his 105th pitch.
Mets RHP Daisuke Matsuzaka is scheduled to make his second start of the season on Wednesday. Left-handed batters are hitting just .093 (4-for-43) against Matsuzaka. ... Cubs top minor prospect Javier Baez is hitting .219 with seven home runs and 25 RBIs for Triple-A Iowa. He is in a 1-for-12 slump. ... Cubs 3B prospect Kris Bryant is batting .351 with 18 home runs and 49 RBIs for Double-A Tennessee. ...Cubs placed C Welington Castillo on the 15-day disabled list because of a rib injury and designated relief pitcher Jose Veras for assignment.