Verdugo had three hits as Boston evened the four-game series at a win apiece. Josh Winckowski (5-5) allowed one run on five hits over five innings for the Red Sox.
Zack Greinke (3-7) allowed four runs on seven hits in 4 2/3 innings for Kansas City.
''It felt good. From top to bottom a lot of really good at-bats,'' Verdugo said. ''We know Greinke. We know he kind of relies on over-aggression and expanding the strike zone. I think we did a really good job of making him come to us and then hitting the mistakes.''
The Red Sox got on the board in the second when ex-Royal Eric Hosmer pulled a double down the right-field line, scoring Verdugo.
Boston added two more runs in the fourth. J.D. Martinez hit a double off the wall in left-center, driving in Bogaerts and Verdugo.
''Greinke is master of throwing pitches around the zone and getting people out,'' Boston manager Alex Cora said. ''He's been really good throughout his career. We had to grind at-bats.''
The Royals threatened in their half of the fourth. They loaded the bases with one out, but Kyle Isbel grounded back to Winckowski, who threw to the plate for the force out, and Nicky Lopez struck out.
''Those drills from day 3 of spring training, that's why you do them,'' Winckowski said. ''When you're (facing the) bases loaded with one out, you're either thinking about a strikeout or a groundout. It just happened to be back to me. Then I had to make another pitch after that.''
Bogaerts drove in the Red Sox fourth run with a two-out single, chasing Greinke.
''(Bogaerts is) really good at going the other way,'' Cora said. ''Today he did it a few times, and it started with the first at-bat. Today was one of those nights when you feel like something good is going to happen.''
Salvador Perez blasted a 454-foot home run to left in the fifth.
Boston got that run back when Reese McGuire drove in Hosmer, who had reached on an error, with a single.
Jarren Duran drove home two with a double in the eighth. The Royals got three in the eighth on Nate Eaton's sacrifice fly and a two-run double by MJ Melendez.
All nine position players in the Royals starting lineup, plus starting pitcher Zack Greinke, were originally signed or drafted by Kansas City. According to Elias, it's just the third game in franchise history - and second this season - in which the Royals have done this. They did it last Friday night at Yankee Stadium and on Sept. 19, 1990 at Minnesota.
Boston: RHP Michael Wacha is nearing his return to the Red Sox. He pitched 4 2/3 hitless innings Thursday night for Triple-A Worcester. He and reliever Chase Shugart combined for the first no-hitter in WooSox history. Cora said Wacha felt good today and likely will get one more start before returning to the parent club.
Kansas City: SS Bobby Witt Jr. was not in the lineup Friday. Manager Mike Matheny said the amount of distance he covered in Thursday's game prompted him to give his prized rookie a rest. Witt was available as a substitute.
The Red Sox and Royals will continue their four-game series Saturday night. RHP Nathan Eovaldi (5-3, 4.11 ERA) will start for Boston. LHP Daniel Lynch (4-7, 4.70 ERA) will get the start for the Royals.
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