The rest of the roster is holding up quite nicely, too.
Betemit's big hit came less than 18 hours after reserve Ramon Santiago delivered a game-ending homer in the 10th inning.
"People wonder why I play so many different lineups, but that's what you have to do when you want to win a division," Tigers manager Jim Leyland said. "You don't win unless you get contributions from everyone, and you have to play them so that they are ready to make a play when you need them."
Austin Jackson went 4 for 4 and scored three times for the AL Central-leading Tigers, who have won seven of 10. Cabrera added two hits and Jose Valverde worked the ninth for his 40th save in 40 chances.
"Austin had a great game for us -- that's exactly what we want from him at the top of the order," Leyland said. "When he's hitting, it is a really big tonic for our offense."
Eric Hosmer had a pair of solo homers for Kansas City, which has dropped four of six.
Jackson sparked the winning rally with a leadoff triple against Blake Wood (5-2). Ramon Santiago followed with a sacrifice fly that trimmed Kansas City's lead to 4-3.
"Alex made the dive, and I couldn't tell if he got it or not until I saw Melky (Cabrera) running after the ball," Royals manager Ned Yost said. "He covered a lot of ground to even get close to that."
"I haven't been swinging the bat well in the last couple games, but this was a big situation," said Betemit, who was acquired from the Royals on July 20. "I know Blake throws hard, so I was looking for something I could hit. He threw me a slider, and I put a great swing on it."
Hosmer connected in the second and the fourth, hitting a drive to right on a 1-2 pitch each time, and Kansas City added two more runs in the sixth to take a 4-2 lead.
"I thought I was pitching well until the sixth -- other than the two homers, obviously," Tigers starter Rick Porcello said. "Things got away from me a little in the sixth, but I was still pleased that I kept us close enough to get the win."
Jackson scored each of Detroit's first two runs, on Young's sacrifice fly in the first and Nate Adcock's wild pitch in the third.
Kansas City helped itself on defense. Rookie Johnny Giavotella made four highlight-reel plays at second base, and Gordon robbed Avila of extra bases with a leaping catch as he crashed into the fence in left.
"We played great defense, but every time you lose a one-run game, you hate it," Yost said. "We had a two-run lead and we couldn't hold it in the eighth."
The teams finish their four-game series with a second straight afternoon game on Thursday. The game -- a makeup of a May 15 rainout -- will feature Detroit rookie Jacob Turner (0-1) making his second career start. Danny Duffy (3-8) goes for the Royals. ... Despite Giavotella's outstanding day in the field, he was replaced by Chris Getz in the eighth inning for defensive purposes. ... Neither starter got a decision. Porcello allowed four runs in seven innings, while emergency starter Adcock gave two in 5 2/3. Adcock replaced Felipe Paulino, who was scratched with back spasms. ... The Royals traded backup C Matt Treanor to Texas during the game. Treanor has been sidelined with a concussion since July 30.