Perez hit a solo homer with two outs in the eighth inning, lifting the Royals over the Texas Rangers 4-3 Sunday.
Perez connected off Keone Kela (4-2) for his eighth home run, barely clearing the fence.
"Everybody else down there is screaming, cheering and high-fiving, but I've got to go out there and worry about throwing strikes," Holland said. "At that point, you just try not to blow the game."
"I try not to get caught up in those moments. I saw him hit the ball and knew it was probably at least a double. I was going out in a tie game or with the lead, regardless. My main objective was thinking about getting (Joey) Gallo the leadoff hitter out."
Holland pitched a perfect ninth for his ninth save in 10 opportunities.
Perez wasn't sure his shot was going to make it over the wall.
"I'm thinking a line drive," Perez said. "I didn't think it was going to be out."
Kela's fastball ran back inside to Perez.
Said Kela: "I know you've got to understand the bitter to enjoy the sweet, but I was being aggressive and I was in the strike zone and throwing strikes. I was confident in all the pitches I throw. I just didn't execute."
Rangers starter Colby Lewis departed after seven innings and 101 pitches, giving up three runs and eight hits.
Kendrys Morales hit an RBI double in the fifth that made it 3-0.
YOST TIES HOWSER
Ned Yost tied Dick Howser with his 404th victory as the Royals manager for second place on the franchise's all-time list. "If Dick hadn't got sick, I don't think anybody would have tied him," Yost said. Howser died of brain cancer in 1987. Yost is closing in on Whitey Herzog's club record 410 victories.
Davis has pitched 106 innings without allowing a home run, the longest active streak in the majors.
Rangers: RHP Ross Ohlendorf (strained right groin) was putn the disabled list. He joins 13 other Rangers on the DL. ... RHP Neftali Feliz (abscess procedure) threw one inning on a rehab assignment Saturday for Triple-A Round Rock, allowing one unearned run on one hit against Oklahoma City. He walked one and struck out one, throwing 24 pitches. ... LHP Matt Harrison (spinal fusion) will make his second rehab start Monday for Round Rock.
Royals: LHP Danny Duffy (biceps tendinitis) will make his first rehab start Tuesday for Triple-A Omaha.
Rangers: After an off-day Monday, RHP Nick Martinez will start the series opener Tuesday at Oakland.