In the space of 20 minutes, Matz's ERA shot up from 1.96 to 4.96.
The left-hander threw 31 pitches, faced eight batters and allowed six earned runs on four hits, including two home runs.
And he hit Bryce Harper on the wrist with a pitch, earning the inning's biggest boos from the crowd at Citizens Bank Park.
"Frustrated to not get out of the first," Matz said after the game.
Only the Mets, Cincinnati Reds and Oakland Athletics have had a starting pitcher allow eight runs without recording an out since the mound was placed at its current distance in 1893. They've now each had it happen twice.
Mets right-hander Bobby Jones did it on Sept. 17, 1997, against the Atlanta Braves.
The last starting pitcher to give up eight runs without recording an out was Cincinnati's Paul Wilson on May 6, 2005, versus the Los Angeles Dodgers. Wilson did it in 2003, as well.
Oakland starter Blake Stein did it in 1998, and so did the A's Bill Krueger, in 1984.
"We didn't make a few plays, first and foremost," Mets manager Mickey Callaway said. "Rough night when that happens."
The Associated Press contributed to this report.