KANSAS CITY — The Red Sox traded for James Paxton to make starts like this.

In the thick of a playoff hunt, the veteran lefty tossed his first quality start in over a month to lead the Red Sox to a 9-5 win over the Royals on Monday at Kauffman Stadium. Boston now trails Kansas City by 1 1/2 games for the third and final spot in the AL Wild Card, and six games behind the Orioles and Yankees in the AL East.

The Red Sox are now 3-1 against the Royals this season, needing just one victory in the final two games to clinch the tiebreaker.

And if the Red Sox are going to make a postseason push, Paxton is going to be a big part of it. The Big Maple, making his second start for Boston since being acquired from the Dodgers, allowed just five hits and struck out four over six innings of two-run ball. Paxton entered throwing his fastball 57% of the time, but attacked Royals hitters differently — using his knuckle curve 41 times (46%) and his fastball just 18 times (20%).

Paxton got an out in the sixth inning for the first time since June 17 by coming back out and facing the heart of the lineup. With a 4-2 lead, the lefty set down Vinnie Pasquantino, Salvador Perez and Hunter Renfroe in order.

“Good fastball, good breaking ball. A lot of strikes. Gave us more than enough,” manager Alex Cora said. “We were debating there in that pocket with Salvy if we were going to the bullpen … He gave up a few rockets one inning before, but he went out there and he pounded the strike zone. I think we learned a lot last year from him. The deeper into the game, the fastball plays better, and that’s what he did.”

Paxton was DFA’d by the Dodgers despite going 8-2 with a 4.43 ERA in 89 1/3 innings because of the return of Tyler Glasnow and Clayton Kershaw, but the Red Sox knew the veteran well from his time in Boston last season and figured he could be a major factor in the team’s playoff race.

He proved his ability to trust his stuff and adapt, with his high knuckle curve usage Monday another example, but he’s also flashed the ability to get better as the game goes along. All 14 of Paxton’s fastest pitches against the Royals came in the fourth inning or later.

“I felt good out there,” Paxton said. “And [for Cora to have that confidence in me and let me go], that was awesome. I’m just competing, giving it everything I got.”

But Paxton couldn’t have done it without his defense. The Red Sox have committed a MLB-worst 84 errors, but flashed the leather in a crucial opener against the Royals. Ceddanne Rafaela made one of the best catches this season in the fifth, taking extra bases away from Maikel Garcia on his 101.5 mph, 409-foot drive to center field. Rafaela leapt, turned his body in the air, reached out and caught the line drive before crashing into the wall.

It even surprised Rafaela.

“I didn’t even realize it,” Rafaela said. “Now I’m seeing it, and I was like, ‘Wow, that was a good catch.’

“I didn’t really think I [was going to have] to make it a back hand [catch], but right there it just happened in the moment.”

Jarren Duran, who laced a clutch go-ahead two-run double in the sixth, also got in on the defensive fun, robbing Hunter Renfroe at the wall with a leaping catch. Dominic Smith added to the highlight reel by making a lunging stop at first, robbing Pasquantino of a hit with Bobby Witt Jr. on the basepaths.

And then there was the offense. The Red Sox, who entered with an MLB best .301 average since the All-Star break, erupted for 18 hits. After Duran’s tide-turning knock — his AL-best 35th two bagger — the Red Sox poured it on. Masataka Yoshida finished with four hits, Connor Wong drove in a pair and Romy Gonzalez blasted a pinch-hit, two-homer 452 feet to center.

Paxton fulfilled his duty with great starting pitching; that’s step one to winning late in the season. But if the Sox can play good defense, and continue to hit the way they have, they will not only be a problem in September, but October as well.

“[The Royals] are going to keep fighting, they have a good team, and it took a lot. … But give our guys credit. They showed up today,” Cora said. “They did their job, and now we have a shot to win the series either tomorrow or the next day.”