KANSAS CITY, Mo. — The Red Sox’ bats gave a little extra on Father’s Day, when their first nine hits against the Royals went like this: Double, homer, double, homer, homer, double, double, double, double.

The strike zone didn’t matter.

If a Royals pitcher threw something close, the Sox hitter took a hack at it. They attacked early in counts and collected eight of their 16 hits on the first or second pitch of an at-bat.

And what finished as a 13-2 triumph and the team’s biggest offensive outburst of the season wrapped up a three-game series win at Kauffman Stadium, in which the Red Sox looked and played like a winning team.

Which begs the question: Do the 31-40 Red Sox still think they can compete this season?

“Well, we have more than half of the season left — things can change around,” said David Ortiz, who ran out of patience with the widening strike zone in his postgame comments Saturday, then slugged his 10th homer yesterday. “We’ve just got to stay consistent. You don’t check out just because the first half of the season didn’t go the way you expected. We’ve got a lot of games left. Anything can happen. In our division, everyone is pretty close. You get a hot month, and things can change.”

The assault began against starter Chris Young (1.98 ERA entering the game) early. Hanley Ramirez cranked one high in the sky that dropped somewhere over the left-field wall for his 15th homer. Ortiz didn’t wait for the umpires to madden him, swinging on the second pitch for a fourth-inning home run to right. Mookie Betts saw a high strike and did what he usually does with those, flinging his hands around and sending it into the left-field bleachers in the fifth inning.

A three-run double from Xander Bogaerts later in the frame cleared the bases and put the Red Sox ahead, 7-0. The floodgates were open.

While the Sox ranked 25th with 3.7 runs per game through their first 60 games, they’ve ranked fifth while averaging 6.0 runs per game over their last 11.

“It’s just 162 games, man, you know what I mean? It all evens out,” Dustin Pedroia said.

Ortiz, who has four homers in 11 games, said, “A couple of us have been able to come back and swing the bat like the team expects us to do. It’s something that I knew was going to happen; it was a matter of time.”

Wade Miley was effectively wild, throwing 60 of his 101 pitches for strikes while inducing the overly aggressive Royals into weak contact. He threw six innings of scoreless ball, allowing five hits and three walks, while striking out two.

If this were a hockey game, three stars wouldn’t be enough.

Betts, who needed a single for the cycle when he flew out to center in the ninth, finished 3-for-5. Brock Holt was 3-for-5 with two doubles and a triple. Pedroia was 3-for-5 with two doubles. Bogaerts was 3-for-5 with three doubles.

The Red Sox finished with 13 extra-base hits for the fifth time since 1914.

“Now we know we can do it,” Betts said. “I think from here on out this will be what we expect of ourselves.”