Pitching in place of Andrew Cashner, whom the Rangers scratched hours before game time due to neck stiffness, Griffin eventually settled down to retire 10 of the final 12 Mets he faced. But the damage was already done for a Rangers team that gave up two runs apiece in the first and second innings.
Griffin refused to blame the short notice for his early struggles.
"I don't want to make excuses about that," he said. "I've just got to be better next time."
Mets rookie starter Chris Flexen had his best game in the Majors in his third start, allowing three runs over 5 2/3 innings for his first career victory.
"It's exciting," said Flexen, who also recorded his first career hit, a double down the left-field line. "The first one's always the toughest, especially with the first two outings being a little rough. Being able to execute a little better today, it's an awesome feeling."
Texas now trails Kansas City and Tampa Bay by four games for the second American League Wild Card spot after all three teams lost on Tuesday.
MOMENTS THAT MATTERED Homer happy at home: d'Arnaud's two-run shot in the second inning cleared the left-field wall on a line, giving him his first home run at Citi Field in almost exactly one full calendar year. That gave the Mets a 4-0 lead, an inning after Cespedes made it 2-0 with his first Citi Field home run since June. A year after hitting a franchise-record 112 home runs at Citi, the Mets are slightly off that pace with 73 in 57 games.
"They're a good hitting team and an aggressive team," Griffin said. "I didn't have my best stuff in the first two innings and they capitalized."
Seeking more history: Now that Beltre has achieved 3,000 hits, the next round number on his agenda is 500 homers. The Rangers third baseman cracked No. 456 off Flexen in the sixth inning, a solo shot that cut the Mets' lead to 4-2. It was the 3,006th hit of Beltre's career, bringing him within one of Al Kaline for 29th place on the all-time list.
"He's played absolutely brilliant defensively. He's exactly what everybody said he was. … At the plate, he's a little anxious right now. He's swinging at a lot of pitches. He'll learn to back off some of them." -- Mets manager Terry Collins on rookie shortstop Amed Rosario, who is 0-for-11 with five strikeouts since starting his career 4-for-14
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Conforto's leadoff homer was the Mets' 10th of the season, most in the Majors. Houston is second with nine leadoff homers.
Chirinos' home run in the ninth was his 13th of the year and tied his career high, which he set in 2014.
WHAT'S NEXT Rangers: As part of the rotation reshuffling in the wake of Cashner being scratched, left-hander Martin Perez had his start moved up and will be on the mound for the 11:10 a.m. CT tilt at Citi Field on Wednesday. Because of Monday's off-day, Perez will pitch on regular rest.
Mets:Rafael Montero looks to avoid his fourth consecutive loss when he takes the mound at 12:10 p.m. ET on Wednesday against the Rangers. Montero, who is 0-2 with a 5.79 ERA in four starts since the All-Star break, must pitch better if he is to hold a rotation spot once Robert Gsellman and eventually Matt Harvey return from the disabled list.