Blackburn was hit hard in the opening frame, as Desmond Jennings singled on the first pitch before B.J. Upton homered on the third pitch and Matt Joyce followed up with a solo shot on the seventh pitch of the night.
"Those first three guys just kind of ambushed me," Blackburn said. "I came out and wasn't where I wanted to be location-wise and it pretty much cost us tonight."
Blackburn, though, was able to regroup after the first, as he cruised until the fifth inning, when he gave up another homer to Upton.
The sinkerballer Blackburn ended up giving up four runs on 11 hits and a walk over six-plus innings. He exited after giving up back-to-back singles in the seventh, but relievers Alex Burnett and Tyler Robertson were able to get out of the inning unscathed.
"Blackie settled in nice, but in that first inning they banged them," Gardenhire said. "We knew that coming in that they were aggressive early, but Blackie couldn't make any pitches early before he settled in nice and got deep into the game."
Rays ace David Price, meanwhile, went seven strong innings, surrendering two runs on seven hits. The left-hander also struck out five batters -- all looking -- and didn't issue a walk.
"I was just trying to throw strikes," said Price, who improved to 15-4 with a 2.50 ERA. "I felt like I was behind in counts more than I have been recently, but I will take the win. Three runs in the first makes my job a lot easier. Our team is playing well right now and that's what I wanted to do, give our team a chance to win today."
The Twins scored in the second on an RBI infield single from Darin Mastroianni after Josh Willingham and Justin Morneau opened the inning with back-to-back singles.
Minnesota scored again in the fifth, when Brian Dozier connected on his sixth homer of the year. The solo shot came on a 1-0 cutter.
"The scouting report was that he [Price] comes at you with a fastball, so that's what I geared up to hit," Dozier said. "So I kind of got in front of the cutter he threw me trying to go backdoor, but I've been working to keep my barrel in the zone longer. He left it up a little bit and I was able to get a pitch to hit."
The Twins wasted a scoring opportunity in the seventh, as they had runners on first and second with one out after singles from Morneau and Mastroianni. But Price struck out Dozier and pinch-hitter Ryan Doumit looking to end the inning.
"I think you saw why that guy is one of the best left-handers in the league," Gardenhire said. "He's filthy. He was going inside-outside, backdoor breaking balls, throwing 96 mph. We put together a couple innings on him, but pretty much got shut down."