NEW YORK -- In order to write Brandon Drury's name on his lineup card Tuesday night, Arizona Diamondbacks manager Chip Hale had to go the old-fashioned route and use "White-Out" to cover up the name of the injured Yasmany Tomas.

Drury and the Diamondbacks then went and scratched out another attempt by the New York Mets to build an elusive winning streak.

Drury homered in the second for the Diamondbacks' first run and Michael Bourn's two-run triple with two outs in the seventh gave Arizona a lead it would not relinquish in a 5-3 win over the Mets at Citi Field.

Hale said he expected Tomas, who developed a stiff neck during Monday's off-day, to start in right field and bat fifth after he went through batting practice. He realized something might be amiss when Drury, who was in the third and final batting practice group, kept asking the manager if Tomas was OK.

"I came in and talked to (Tomas) and he said he just didn't feel like he could give us 100 percent," Hale said. "Drury kept asking 'Is Tomas going to play?' I said, well I guess I've got to put Drury in the lineup because he keeps asking. He answered it."

Drury finished 2-for-4 and helped out with his glove as well in the third inning, when he made a diving catch to rob Mets pitcher Steven Matz of an extra-base hit.

"I had just heard that his neck was sore, so I was just asking around to see what the deal was so I had an idea (and) wasn't caught off-guard last-minute," Drury said.

Homers by Drury and Paul Goldschmidt in the sixth inning gave the Diamondbacks a 2-1 lead before a two-run homer by Neil Walker in the bottom of the sixth put the Mets ahead and left ace Zack Greinke, who was activated from the disabled list earlier in the day after missing five weeks with a left oblique injury, in danger of suffering the loss.

But the Diamondbacks scored three times -- all with two outs -- while sending eight batters to the plate in the seventh against Hansel Robles (5-4). Bourn's triple scored Chris Owings, who led off with a double, and Phil Gosselin, who drew a one-out walk while pinch-hitting for Greinke.

Bourn is batting .279 with 22 RBIs in 61 at-bats with runners in scoring position and just .232 with three RBIs in any other situation.

"(Bench coach) Glenn Sherlock and 'Mags' (hitting coach Dave Magadan) were sitting next to me (and) I said 'even when he's struggling, he gets his hits in the good time or a big time of the game,'" Hale said of Bourn. "And sure enough, boon. He hits a triple. He's been very, very clutch for us."

Bourn scored on an RBI single by Goldschmidt before a trio of Diamondbacks relievers combined to preserve the win for Greinke by limiting the Mets to one hit over the final three innings. Jake Barrett worked around a two-out walk in the ninth to earn his fourth save.

Greinke (11-3) allowed three runs on five hits and one walk while striking out six over six innings for the Diamondbacks (46-66), who went 9-22 while he was on the disabled list.

"It's been pretty awful, hopefully, it gets better from here," Greinke said. "Today was about as good as it gets. Everything kind of clicked. Scored some runs, the starter pitched semi-deep, semi-decent and the bullpen did great. Got a win."

The Mets (57-55) are still in search of that winning formula. New York, which fell 2 1/2 games behind the Miami Marlins in the race for the National League's second wild card, has not won consecutive games since July 7-8. It is 10-17 since that "winning streak."

"We've just got to keep going out there, keep grinding and hope we get hot," said Walker, who had three of the Mets' six hits and two of their runs. "But certainly, nights like tonight can be frustrating."

James Loney had an RBI groundout in the first for the Mets.

Left-hander Steven Matz allowed two runs on five hits and one walk while striking out nine over six innings. Matz, who has won just once in his last 13 starts, threw a career-high 120 pitches, including 27 in the first inning.

"I thought after that he really settled down and started making pitches," Mets manager Terry Collins said.

NOTES: The Diamondbacks placed C Wellington Castillo on the paternity leave list and recalled C Oscar Hernandez from Double-A Mobile. Castillo will miss the entire series after his wife gave birth to the couple's second child, a son, on Monday night. ... Diamondbacks OF A.J. Pollock (broken right elbow) continued his rehab assignment Tuesday by serving as the DH for Single-A Visalia. ... Mets LF Yoenis Cespedes (right quad strain) took batting practice Tuesday at the team's spring training complex in Florida. ... Mets 3B Jose Reyes (left oblique strain) did not begin a rehab assignment as originally scheduled Tuesday because he is still unable to swing a bat from the right side.