Mets manager Mickey Callaway and second baseman Robinson Cano congratulate...

Mets manager Mickey Callaway and second baseman Robinson Cano congratulate Amed Rosario on a solo home run against the Twins during the third inning of a game on Wednesday at Target Field in Minneapolis. Credit: Getty Images/Hannah Foslien

MINNEAPOLIS — A dozen runs in the late innings to complete a rare road sweep meant plenty of highlights for the Mets, but only one inspired outright awe.

Pete Alonso’s moonshot halfway up the third deck in leftfield, his 31st home run of the year, served as the climax of the Mets’ 14-4 win against the Twins.

Winners of four consecutive games, matching their season high, the Mets have come out of the All-Star break with two road series wins in a row, matching their first-half total. And this one came with plenty for the Mets (44-51) to be happy about: Dominic Smith’s go-ahead, pinch-hit homer and career-high four RBIs, Jeurys Familia’s second successful relief appearance in as many days, and Amed Rosario’s four hits and three RBIs.

All positive, none majestic. Alonso’s homer landed an estimated 474 feet from home, the longest Mets long ball since at least 2015, when MLB’s Statcast began measuring them, and longer than any of the 57 he hit in the Home Run Derby last week in Cleveland.

“It’s not every day,” Alonso said, “you connect like that.”

Said manager Mickey Callaway, who frequented Target Field as the Indians’ pitching coach: “I’ve seen a lot of BPs in here and people don’t even hit them there in BP. That’s pretty impressive. He put better swings on the ball today. I thought something was due, and there it was. He hit that one a long way. It was fun to watch.”

Did Alonso know he hit it well enough for it to land where it did?

“I don’t know,” he said. “That’s why I gotta watch it a little bit.”

This one came at a good time, too. Alonso had been 1-for-17 with 10 strikeouts in five games to begin the second half. His 54th extra-base hit gives him another Mets rookie record, and he is 10 homers away from tying the single-season franchise record held by Todd Hundley and Carlos Beltran.

Lefthanded starters Jason Vargas (six innings, three runs) and Martin Perez (six innings, two runs, one earned) kept it close into the late innings. The Mets didn’t take a lead until the seventh. Smith, pinch hitting for J.D. Davis with Perez out of the game, snuck a homer over the 23-foot wall in rightfield.

“Having Dom come off the bench is a valuable thing,” Callaway said. “That was good to see. That kind of put things where we needed to be.”

It turned into a blowout in the eighth, when the Mets scored a half-dozen unearned runs. With two outs, Adeiny Hechavarria skied a ball to leftfield, where Eddie Rosario dropped it. Two runs scored. The Mets piled on from there: Jeff McNeil RBI double, Smith RBI single, Alonso homer.

The Mets added three runs against utility player Ehire Adrianza, who struck out Smith with a 62-mph pitch that registered as a curveball.

“Ruined my day,” Smith joked.

The offensive outburst made it unnecessary for Callaway to navigate the final frames with a bullpen at less than full strength. Closer Edwin Diaz and Robert Gsellman were unavailable, though Seth Lugo was ready to pitch — for a fourth time in five days — if needed.

When the score was still close, Jeurys Familia tossed a scoreless seventh, allowing a single to Marwin Gonzalez but getting Luis Arraez to ground into a double play. That came a day after he retired the only batter Callaway asked him to get in a win Tuesday.

“We saw the ground ball we’ve been looking for finally go to somebody and get a big double play,” Callaway said. “That’s what he’s going to do when he gets outs.”

Familia (7.11 ERA)  said: “The last two days have been really good. I’ve been feeling as good as I’ve felt all year. This is how I expected to pitch.”

FAR GONE CONCLUSION

Pete Alonso’s eighth-inning moon shot was the longest by a Met since Statcast began tracking distance in 2015. Longest Mets HRs since then:

1. Pete Alonso 474 feet

2. Michael Conforto 472

3. Yoenis Cespedes 463

4. Justin Ruggiano 461

5. Alonso 458