ST. LOUIS -- Kodai Senga had five strikeouts on Saturday night, but the first was a big one.

It came when Senga caught Paul Goldschmidt looking with a 95.3 mph fastball that caught the outer edge of the strike zone in the fourth inning. It was his 150th punchout of the season.

Senga became just the seventh pitcher in Mets history to hit the 150-strikeout mark in his rookie season, joining Noah Syndergaard (2015), Dwight Gooden (1984), Jon Matlack (1972), Gary Gentry (1969), Jerry Koosman (1968) and Tom Seaver (1967).

He also became the fifth pitcher of Japanese origin to hit the milestone as a rookie.

“The biggest goal for me has been just staying healthy, and hitting 150 strikeouts just comes with staying healthy,” Senga said through an interpreter. “I still have a little bit of the season left, so I just want to maintain that.”

More importantly for Senga, the Mets rolled to a 13-2 win to claim the first three games of a four-game set against the Cardinals at Busch Stadium.

Senga (10-6) turned in his fourth quality start in his past five outings, allowing a single run in seven innings. He allowed just two hits and walked two, and 55 of his 97 pitches were strikes in his longest outing since July 5, when he threw eight innings.

“He's been solid,” Mets manager Buck Showalter said. “You know I can sit here and critique a lot of things that he's doing and where he is in the season and everything that he's done to get here, but I think we've got it well documented. He continues to be solid for us.”

He was able to pitch around his own error in the first and leadoff walks in the second and fifth innings. The lone run Senga gave up was a homer to Nolan Arenado in the fourth.

While the numbers are good, Senga said he wasn’t completely happy with the performance and credited catcher Francisco Alvarez for helping him get through it.

“I think I just wasn't able to control myself, my body and my pitches as well as I wanted to, but Alvy did a really good job putting me back on track,” Senga said.

The Mets bats gave him plenty of support as they hit at least two homers for the sixth straight game, tied with four other teams for the longest such streak this season.

Daniel Vogelbach’s grand slam in the fifth ended the night for Cardinals starter Miles Mikolas (6-9) and put the game out of reach at 7-1. It was his fourth career grand slam and his third homer in his past seven games.

“You have stretches where you don't hit well, and you have stretches where you struggle, but if you stay the course, you know things will come back to life, and I feel like I just started to put some games together here,” Vogelbach said.

DJ Stewart hit a solo homer in the fourth, and Pete Alonso hit a two-run moonshot off Andrew Suárez that traveled 466 feet into the center-field bleachers to give the Mets a 9-1 lead in the seventh.

Francisco Lindor and Jeff McNeil each continued their hot hitting with seven combined hits.

“Good starting pitching, timely hitting, and we got guys leading us like Lindor, who's been on an unbelievable stretch, and [Brandon] Nimmo and Pete [Alonso], Jeff [McNeil] is doing what he does, and we’re just playing good baseball,” Vogelbach said.

Lindor had three singles, a double, an RBI and scored three times. McNeil drove in Lindor with his second hit, and the duo combined for a double steal, with Lindor stealing home, to give the Mets a 1-0 lead in the first.

“Both those guys are really coming on, and you know, chasing what they've done all year, all their career,” Showalter said. “So that's been good to see.”

The Mets have won four straight and six of their past seven. New York will look to complete its third road series sweep of the season and first in a four-game series on Sunday.

“At this time of year, when you can bring a lot of intensity and energy and want to, and some guys are trying to, you know, make their mark a little bit and get some traction for not only this year, but next year, and sometimes you benefit from that,” Showalter said. “There's been a lot of frustration in our clubhouse over the year. And I think sometimes you kind of take it out there with you. I think everybody needs a little edge to them.”