Ogando quickly settled down, scattering six hits over 7 2/3 innings to remain unbeaten, Adrian Beltre homered, and the Texas Rangers avoided a three-game sweep by Detroit with a 7-3 victory over the Tigers on Wednesday night.
Detroit had 21 runs and 38 hits while winning the first two games of the series and had taken four straight overall.
But the Tigers couldn't get much going against Ogando (7-0), who struck out seven to match a career high and walked two.
Kelly, the game's second hitter, ripped his first homer of the season on a 2-0 pitch into the seats in right.
Ogando struck out four of the next seven batters he faced and became the first major league pitcher to win his first seven decisions as a starter since Jered Weaver went 9-0 for the Los Angeles Angels in 2006.
"I fell behind in the count," Ogando said through an interpreter of Kelly's at-bat. "I left the pitch right over the plate. But I never gave up. I never got my head down. I just kept throwing and kept battling.
"I just wanted to keep my composure. Sometimes you get down but you have to keep throwing and do the best job you can."
"After we scored some runs he settled down and located his pitches a little bit better," Rangers catcher Yorvit Torrealba said.
Elvis Andrus had three hits for the AL West-leading Rangers.
Phil Coke (1-6) gave up six runs -- four earned -- and 10 hits in five innings in his return to Detroit's rotation. Coke was recalled from an injury rehab assignment with Triple-A Toledo and was reinstated from the 15-day disabled list before the game.
Coke, a converted reliever making his 11th start in 170 big league appearances, had been out since May 24 with a bone bruise on his right foot, and the rust was apparent.
"I think he was a little sluggish," Tigers manager Jim Leyland said. "He made some bad pitches when he had the count in his favor."
The Tigers failed to complete their first three-game road sweep of the Rangers since May 1-3, 2001.
But Detroit wrapped up a 4-2 road trip against the Chicago White Sox and Rangers heading into an eight-game homestand that gets under way Thursday night against Seattle.
"We won four of six against two excellent teams," Leyland said. "That's a good week's work. You don't ever sound satisfied, but I think if we win four of six on the road the rest of the way, I'll be very tickled."
The Rangers loaded the bases in the third on three straight singles. Craig Gentry then hit a chopper to third baseman Kelly, who threw wildly to the plate for an error, allowing Torrealba to score. Catcher Victor Martinez retrieved the ball about 20 feet behind the plate and threw to Kelly covering home, but Kelly failed to catch the ball cleanly and Chris Davis was safe as the two collided.
Hamilton followed with a two-run double to stretch the Rangers' lead to 4-1. Andrus, who had fresh legs after getting the previous game off, added an RBI single in the fourth, and Beltre's run-scoring single in the fifth made it 6-1.
Beltre led off the seventh against Adam Wilk with his 12th homer off the left field foul pole.
Andrus was caught stealing in the first inning, breaking a streak of 19 straight successful steals this season. ... The Rangers fired hitting coach Thad Bosley and promoted Scott Coolbaugh, who had been hitting coach for Triple-A Round Rock. Bosley, a former major league outfielder, was in his first season on manager Ron Washington's staff. ... To open a roster spot for Coke, the Tigers optioned C Omir Santos to Toledo. ... Former Rangers LHP Kenny Rogers has been elected to the team's Hall of Fame and will be inducted on Aug. 6. ... Texas placed 2B Ian Kinsler on the paternity list after his wife Tess gave birth to a son, their second child, on Wednesday afternoon. Davis was recalled from Triple-A Round Rock and Michael Young started at 2B.