But the Rays nixed that in the seventh inning, when they plated five runs -- three of which were unearned -- to pull even farther ahead and take the hard-fought 7-4 win.
"A big inning hurt us again today," manager Ron Gardenhire said. "Blackie was throwing the ball pretty good, matching numbers with [Rays starter James Shields]. ... You put up a crooked number and you can't recover from it."
The inning started with a routine single to right field by Carlos Pena, and it went downhill from there.
With two runners on base and no outs, Blackburn botched a throw to first base on an infield hit by Jason Bartlett. The error allowed the first run of the inning to score and kept two runners on the basepaths.
Blackburn said the miscue -- an error that may have lost the game for the Twins -- was a result of not having a good grip on the ball and trying to rush the throw to make the out.
After Sean Rodriguez grounded out, Blackburn intentionally walked Carl Crawford to load the bases. Blackburn remained in the game to face Evan Longoria -- a move that was questioned, considering the third baseman recorded an RBI hit off the pitcher earlier in the game -- who hit a single up the middle to score two more runs, bringing the unearned run total to three and ending Blackburn's night with the Twins down, 5-1.
Brian Duensing came in and gave up a hit to Gabe Kapler that scored two runs, bringing Blackburn's run total for the outing to seven.
Despite the outcome, however, Blackburn thought he pitched well and wouldn't change his decisions on the mound if given another chance -- especially his and Gardenhire's choice to have him face Longoria.
"He's another guy where I probably left it over the plate a little bit, and another ground ball just got through," Blackburn said. "It's frustrating, but I wouldn't change a whole lot about what happened."
The Twins did what they could to salvage the inning, and came back in the bottom of the frame with hot bats.
Justin Morneau started a streak in which the Twins got five consecutive runners on base with a single to left-center. Jim Thome's single off the right-field wall later in the inning brought in two runs and riled up the 40,328 fans at Target Field.
Those two RBIs brought Thome's career total to 1,592, moving him past Hall of Famer Andre Dawson and into 34th on the all-time list.
Delmon Young would add a hit and an RBI, but that was all the Twins would score.
Minnesota had only one baserunner in the final two innings, with Young reaching on a double in the ninth.
"We're not getting the big hits as consistently as we need to," Morneau said. "We've been missing those hits. You can look at our numbers, the runners in scoring position and all that stuff, and we haven't done as well there as we need to."
Gardenhire knew his team had some blown chances, saying that when teams make mistakes against the Rays, "they will make you pay for it."
He added that the Twins played neck-and-neck with their opponent, but one inning or one play seemed to make the difference in each of the four games in this series.
The Twins finished their seven-game homestand with a record of 3-4, and the series loss to the Rays was only their third one at home.
Rays manager Joe Maddon knew his team had done something special by beating the Twins at home, and he wasn't shy about admitting it.
"Winning three out of four here is really not an easy thing to do," Maddon said. "They're so good, and they've got this new facility. Their record at home has been great.
"They're good. Hey, they fight, man. The Twins fight. You've got to be ready to play here."