Kinsler homered in the first inning, hit a bases-loaded triple in the third that made it 9-0 and also singled. Texas had 11 hits by the third, including six for extra bases.
"It's tough as an offense to have every single guy going well," Kinsler said. "Right now it's happening. It seems like we're seeing a lot of pitches and making the pitchers work."
The Rangers, who have outscored opponents 39-12 during their winning streak, got 14 hits. The only Texas player without one was Adrian Beltre, who went 0 for 4 a day after hitting for the cycle.
"They've been doing that a lot for everybody, getting four or five runs in an inning," Dempster said. "The game plan is still the same. But you have a little leeway when one run is not going to change the game."
The AL West leaders have won eight of nine against the Twins this season.
"We're swinging the bat pretty well," Moreland said. "One through nine, there are no breaks."
Justin Morneau went 4 for 4 with a home run for Minnesota, which has lost five in a row and 14 of 16 overall.
Dempster allowed two runs in six innings and improved to 3-1 since he was acquired from the Cubs on July 31. He was 5-5 with Chicago.
After two shaky outings in his first three starts with Texas, Dempster has yielded just three runs in 14 innings over his last two starts. He struck out seven and walked two to beat the Twins for the second time this season.
Brian Duensing (3-9) gave up a career-worst nine runs in 2 1/3 innings. It was another disappointing outing for Minnesota's starting pitchers this series -- they have allowed 18 earned runs and 24 hits in 9 2/3 innings.
"It was really tough," Duensing said. "I had a bad day that came at the worst possible time."
Duensing was coming off one of his best outings of the season, having held Oakland to two runs in six innings on Monday. But the left-hander got off to a rough start when Kinsler drove his third pitch into the seats in left. It was Kinsler's 25th career leadoff homer.
Nelson Cruz added an RBI double in the first to make it 2-0.
Moreland's three-run homer in the second inning was the third-longest shot at the Rangers' stadium. Josh Hamilton hit the longest, a 490-foot drive in 2010.
Moreland made his first start against a left-hander this season.
"I come in every day ready to play," Moreland said. "I saw my name in the lineup and went out like I do every day."
Morneau's 17th home run of the season in the fourth was the first homer by Minnesota since Aug. 17. In the sixth, Morneau was thrown at home by Craig Gentry trying to score on a single to center.
Texas RHP Yu Darvish who missed his last start with tightness in his right quadriceps, threw a 30-pitch bullpen session and took fielding practice before the game. He will throw again in the bullpen Sunday ahead of his scheduled start Tuesday against Tampa Bay. ... Twins LF Josh Willingham was back in the lineup after missing two games with a stiff neck. ... Rangers manager Ron Washington said RHP Koji Uehara (strained right lat) may come off the disabled list Sunday if he has no setbacks after throwing a scoreless inning of relief for Triple-A Round Rock. ... Ben Revere became the fourth player in Twins history with consecutive 30-stolen base seasons. ... The Rangers gave away Washington bobblehead dolls to 30,000 fans. "It's a pretty good likeness," Washington said.