"Just like we drew it up," Rangers manager Ron Washington said.
"I figure if you're 40 years old, you're going to be in a lot of history books about something," Oliver said. "If Arthur (Rhodes) gets a save tomorrow, he'll be the oldest."
The Rangers put 22-year-old closer Neftali Feliz on the 15-day disabled list earlier Saturday because of right shoulder inflammation. They then purchased Eppley's contract from Triple-A Round Rock and said they would go closer by committee until Feliz returns.
That includes Oliver, who made his 602nd career appearance, and 41-year-old Arthur Rhodes, who hasn't had a save since 2008 and has only eight in 855 career games. Before a save last season, Oliver hadn't had a save since 1994.
Ogando (3-0) held the Royals scoreless until Kila Ka'aihue led off the seventh with a homer on the right-hander's 14th and final pitch. He struck out five, walked one and allowed five hits.
"I used changeup early in game and keep hitters out of bounds," Ogando said. "I didn't have my control of my pitches in the early innings. But I kept pounding the strike zone."
By losing the first two games in the three-game set, the Royals (12-9) became the last team in the majors to lose a series this season. They had won three series and split three others before getting to AL West-leading Texas.
Kansas City had two runners on in each of the first three innings without scoring. Billy Butler, who entered hitting .352, left runners in scoring position in the first and third with an infield popout and then a strikeout.
`We couldn't capitalize, and I'm speaking of myself," Butler said.
After Elvis Andrus had a one-out walk in the third off Kyle Davies (1-2), Michael Young had his second single of the game. Adrian Beltre then hit a sacrifice fly before Young stole second base and scored on a single by Nelson Cruz to make it 3-0.
Davies, who needed 79 pitches to get through the first three innings and only 33 over the next three, limited the Rangers to three runs and four hits over six innings. The right-hander has still never beaten them, now 0-5 with a 5.91 ERA in eight career starts.
"I wasn't very effective the first three innings, trying to be too fine," Davies said. "I settled down in the fourth, fifth and sixth, but the damage was done."
After Ka'aihue's homer, Eppley came on and struck out Matt Treanor. Eppley allowed only two hits.
"When he came out of the bullpen and I welcomed him to the big leagues and I put my hand on him and he didn't have any nervous energy," Washington said. "He was ready to go. And the results proved just that."
Alex Gordon extended his career-best and AL-high hitting streak to 17 games for the Royals with a single in the first.
Gordon's single came after a single by Melky Cabrera, but Ogando got out of that jam with an infield popout and a grounder. The Royals had two runners on in each of the first three innings.
After Cabrera doubled and Gordon was hit by a pitch to start the third, Ogando, a converted outfielder, faced only 12 more batters -- helped by a double play in the fifth -- before Ka'aihue's second homer landed in the second deck of seats in right field.
Texas got an unearned run in the second when David Murphy reached on an error by second baseman Chris Getz and scored on a double by Mitch Moreland.
Young, the longest-tenured Ranger in his 11th season and now the team's primary designated hitter, is hitting .434 (23 of 52) in a 13-game hitting streak to push his season batting average to .366.
While Gordon extended his hitting streak, the second-longest active in the majors behind a 20-gamer by Andre Ethier for the Los Angeles Dodgers, Royals teammate Jeff Francoeur has a 13-game hitting streak after his eighth-inning double. Wilson Betemit's 13-game streak ended by going 0 for 4, including shortstop Andrus making an impressive catch of a popup in short left field to end the eighth.