Gee (8-1) recovered from a shaky start in the follow-up to his only loss of the season. Making his first appearance against the Rangers, he allowed three runs and eight hits with two walks.
Gee, who walked a career-high six over four innings in his previous outing, has given up only eight earned runs in five June starts. He grew up in north Texas and played college ball at Texas-Arlington.
Daniel Murphy added three hits for the Mets, who have won four of five overall and took two of three from the AL West leaders to open a key stretch of 13 of 16 games on the road.
Texas' Michael Young homered in his third straight game to match a career high, extending his hitting streak to 12 games. Young had three RBIs.
The Mets scored a run in the first off Derek Holland (6-3) when Reyes reached on an infield hit, stole second, advanced to third on a flyout and scored on a passed ball.
Gee retired the first two batters in the first, but Young hit his fourth homer in five games and Mitch Moreland added an RBI single for a 2-1 Texas lead.
Later in the inning, Reyes' RBI single and Carlos Beltran's two-run single gave the Mets a 5-2 edge.
Young's run-scoring single in the fifth pulled the Rangers within 5-3.
In the sixth, Murphy's run-scoring double and Ruben Tejada's RBI single padded the Mets' lead to 7-3.
Pitching coach Mike Maddux was making a visit to the mound and made a comment to Fletcher. Washington, who had earlier argued two close plays on the bases that went against the Rangers, ran onto the field and was quickly tossed by Fletcher.
Andrus, who wasn't in the game due to a sprained left wrist, was also thrown out for yelling at Fletcher from the dugout.
Holland gave up seven runs — three earned — in six-plus innings.
Texas scored twice in the ninth against Francisco Rodriguez on Endy Chavez's RBI double and Young's run-scoring grounder.
The Mets had 22 runs and 31 hits in the final two games of the three-game set.
NOTES: Rangers OF Josh Hamilton was given the day off after striking out four times in Saturday's 14-5 loss. The reigning AL MVP is batting .115 in day games this season. He tried contact lenses on Saturday to combat the glare, but scrapped the idea before his final at-bat because he was having problems with depth perception. ... Andrus sat out his second straight game and isn't sure when he'll be back in the lineup. He said the injury isn't serious enough for him to need to go on the disabled list. ... Mets LHP Jonathon Niese will be examined by a cardiologist Tuesday in Detroit after experiencing a rapid heartbeat during Saturday's start. The Mets say the exam is strictly precautionary. ... LF Jason Bay (stiff neck) and 3B Justin Turner (jammed thumb) were back in the New York lineup after missing Saturday's game.