The fifth-inning shots by Kubel and Thome kept the Twins 3½ games ahead of Chicago in the AL Central. The White Sox beat Detroit 5-4 in 10 innings.
Thome's blast hit off the top of the American flagpole beyond the right-field bleachers at Target Field. He is one homer shy of Frank Robinson for eighth all-time.
The homer by Thome traveled so far and was so high, it required multiple viewings by the Twins public relations staff to get an accurate estimated distance. It was eventually announced at 480 feet.
With the score 2-all, Kubel hit a two-run homer off Sean O'Sullivan (2-5). Thome connected one batter later.
Kevin Slowey made his first start for the Twins since injuring his right triceps on Aug. 21. He threw 77 pitches in four innings, and allowed two runs and seven hits.
Five different Twins relievers helped preserve the victory, Minnesota's 17th in its last 20 home games.
The Royals play both the Twins and the White Sox this week and manager Ned Yost said before the game that he plans to play his best players in each game.
"In fairness to Minnesota and Chicago, we're playing everyone at their best position," he said. "Of course I have guys I want to look at and evaluate in certain situations, but we're going to do that more after this week."
The Royals certainly didn't look like a team that was just playing out the string.
After the Twins went ahead in the fifth, an RBI double from Pena and a groundout by Betancourt made it 5-4.
Notes: The Twins are 10-3 against the Royals this season. ... Twins manager Ron Gardenhire said that 3B Danny Valencia's hamstring continues to improve, but the team wants to give him extra time to make sure he doesn't sustain a more serious injury when he returns. ... Gardenhire also said INF Nick Punto is about four or five days from coming off the disabled list (hamstring). Reliever Brian Fuentes (back) threw on Monday and should be available soon. ... The Royals called up OF Jarrod Dyson from Triple-A Omaha on Monday. He was the Royals' 50th-round draft pick in 2006. ... Royals utility man Willie Bloomquist missed the game to attend to a personal matter back home. Yost said Bloomquist should return on Tuesday or Wednesday. ... Billy Butler has hit safely in 90 consecutive series, tying the Royals' club record set by Willie Wilson from 1979-81.