Rene Tosoni's sixth-inning grand slam 4 count in the second of three between the clubs.
Anthony Swarzak (4-7) allowed 10 hits and two runs while fanning six over 6 1/3 innings for the win.
Johnny Giavotella hit two doubles and a triple for the Royals, who saw their two-game win streak snapped.
Sean O'Sullivan (2-6) was tagged in defeat for nine hits and six runs over five-plus frames.
Minnesota pulled away for good and chased O'Sullivan in the deciding frame, as Danny Valencia, Parmelee and Trevor Plouffe struck consecutive singles before Tosoni brought everyone home with a blast to right on Vin Mazzaro's first pitch to make it 7-2.
"I was just trying to tighten the zone. It was a heater, middle-down," Mazzaro said of the fateful pitch. "I just left in back over the plate."
Kansas City did not die hard, tallying two runs in the ninth off Joe Nathan on a Jarrod Dyson sacrifice fly and RBI hit from Billy Butler. Giavotella, who tripled in the prior at-bat and scored on Butler's single, reached after Span -- who had missed more than a month after suffering a concussion -- collided with the wall in center.
"I was a little shaken up. I'm not going to lie. I was more upset that I missed the ball to be honest," Span admitted. "I didn't know whether or not I was going to think twice about going into walls, or running into catchers, but I play the game hard."
Eric Hosmer fanned swinging to end the game.
Lorenzo Cain singled in Salvador Perez in the second, but Parmelee's homer tied the game to kick off the home half.
In the fifth, back-to-back RBI triples from Span and Revere made it 3-1, but Butler doubled to begin the Kansas City sixth and later scored on a Perez groundout.
With a 2-for-4 performance, Parmelee raised his average to .351 with four home runs and 13 RBI since his call-up from Double-A New Britain on September 6...Plouffe totaled three hits...Prior to the game, the Twins claimed pitcher Esmerling Vasquez off waivers from the Diamondbacks and transferred infielder Alexi Casilla to the 60-day disabled list...Also before the contest, the Royals dealt infielder Kila Ka'aihue to Oakland in exchange for minor league hurler Ethan Hollingsworth.