SAN FRANCISCO -- When Rene Rivera made a sliding catch while crashing into the backstop on the New York Mets' first defensive play of the game Sunday, the veteran catcher assured himself a spot on the club's daily highlight reel.

Little did he know the best was still to come.

Rivera hit two home runs and made a key defensive play on a steal attempt, leading the Mets to an 8-2 victory and a three-game sweep of the San Francisco Giants.

Right-hander Rafael Montero limited the Giants to one run in 5 2/3 innings for his second career win, helping the Mets record their second road sweep of the season and first in San Francisco since 2013.

"We got here and we wanted to do something good," said Rivera, whose club was swept in four straight by the Los Angeles Dodgers to start the week. "Coming here and sweeping San Francisco, that shows a lot about the chemistry and the demeanor of this team."

Rivera, who began the day with just three homers, smacked a two-run shot in the second inning and a solo blast in the fourth, both off Giants left-hander Matt Moore.

"It was funny because (hitting coach Kevin Long) and I, we talked a couple of weeks ago that I never had had a home run (off) the same pitcher twice," Rivera said of the 15th multiple-homer game by a Met this season. "Today was the day. I just wanted to help the team win and do something good."

Jay Bruce added a two-run homer in the eighth inning and Curtis Granderson a solo shot in the ninth, increasing New York's total of road home runs this season to a major-league-best 68.

The four homers gave the Mets 46 in June, a franchise record for a single month. New York still has four games remaining in the month. The Mets' previous record for home runs in a month was 45, set initially in August 2015 and tied in August 2016.

Montero (1-4), who was making his 15th career start, was supported by an error-free defense and a potential rally-killing play by Rivera while protecting a lead his teammates gave him in the top of the first inning.

He allowed five hits and two walks in his 104-pitch outing in improving his career record to 2-9. Montero struck out a season-best seven.

"I hope this is who you see from now on because his stuff's good enough," Mets manager Terry Collins said of Montero, whose previous two outings had been in relief. "Hopefully this is a huge wake-up call that he can pitch in this league."

After the Giants scored on a bases-loaded sacrifice fly by Buster Posey to get within 3-1 in the third, Montero caught a break when Rivera threw out Hunter Pence trying to steal second base with San Francisco's leading home run hitter, Brandon Belt, at the plate with a full count.

The out ended the inning, stranding Joe Panik at third base.

"I didn't send him," Giants manager Bruce Bochy said before coming to Pence's defense. "We can't keep laying back. We've got to force the issue a little bit."

Five New York relievers picked up Montero with 3 1/3 innings of one-run, four-hit ball.

Bruce and Rivera finished with three RBIs apiece for the Mets, who have hit 27 home runs in their past 14 games.

Bruce, Rene Rivera, Granderson, Asdrubal Cabrera, Wilmer Flores, Lucas Duda and T.J. Rivera had two hits apiece for New York, which outhit the Giants 14-9.

The Mets stranded 15 baserunners, the Giants eight.

Moore (3-8) was pulled after 4 1/3 innings, having allowed five runs and seven hits. He walked two and struck out five.

Denard Span and Pence had two hits apiece for the Giants, who lost their fifth in a row and 12th in their last 13 games.

Posey drove in the two runs with a sacrifice fly and an infield out. Three of Posey's at-bats came with a total of eight runners on base. He popped out into a double play on the other occasion.

"These are tough times. No getting around it," Bochy said. "I've been around a long time. This is as tough as I've ever been around. The baseball gods are really testing this group. Enough is enough."

NOTES: Mets LF Michael Conforto left the game in the sixth inning after having been hit by a pitch on the left hand. X-rays taken during the game were negative. ... The Mets announced before the game that OF Tim Tebow had been promoted from low Class A Columbia to high Class A St. Lucie. The former Heisman Trophy winner hit .222 with three home runs and 23 RBIs in 212 at-bats at Columbia. ... Giants LF Austin Slater was removed from the game in the seventh inning after experiencing tightness in his right hip flexor. ... Giants RHP Hunter Strickland returned to the active roster Sunday after serving his six-game suspension for his involvement in a fight with Washington Nationals RF Bryce Harper on May 29. He served up CF Curtis Granderson's home run ... The Mets are off Monday before beginning a three-game series at Miami. ... The Giants continue a six-game homestand Monday night with the first of three against the Colorado Rockies.