"It's not fun to lose and go home with a loss but, in time, I'll be able to look back and understand and appreciate what this day is about," Carroll said.
The home run -- on a 2-2 sinker -- was Carroll's first since Aug. 9, 2009, also coming at U.S. Cellular Field. It snapped a homerless streak of 1,348 at-bats, which was the longest drought among active players.
The ball landed in the left-field bullpen and was later retrieved by Twins left fielder Darin Mastroianni for Carroll, who admitted he didn't know if it was gone off the bat.
"I was just hoping it'd stay fair and then I came around first and saw the umpire give the signal," Carroll said. "I know it's going to be something fun for my family, especially my son. Every day he asks me who hits home runs for both sides and finally today I can say I did."
Carroll wasn't the only player to homer Monday. White Sox second baseman Gordon Beckham drove in three of Chicago's four runs, two on a homer in the bottom of the fifth.
Beckham hit an 0-2 fastball from Twins right-hander Samuel Deduno (5-3, 3.66 ERA) into the left-field seats, also scoring A.J. Pierzynski. It was one of Deduno's lone miscues, as he allowed only five other hits in six innings. He also struck out three, walked three and evaded three other potential threats.
A single by Alejandro De Aza and consecutive walks loaded the bases in the second for the White Sox after Beckham's two-out homer, but Deduno induced an inning-ending groundout.
Chicago also left two on with one out in the first inning and runners at second and third with two gone in the fifth without scoring.
"He can throw a breaking ball over at just about any time, his fastball moves all over the place," Twins manager Ron Gardenhire said. "He just has great stuff and if he gets himself in a few messes, he can get himself out of them with that stuff."
Like Deduno, the White Sox bullpen evaded trouble after relieving starter Hector Santiago.
Santiago (3-1, 3.71) exited after walking Mastroianni and Joe Mauer to open the sixth, bringing in right-hander Nate Jones. Pierzynski nabbed Mauer at second on a double steal, Jones got Josh Willingham to pop up to third and lefty Donnie Veal struck out Justin Morneau to escape further damage.
The Twins also had a chance in the seventh, putting two on with one out, but pinch-hitter Ryan Doumit grounded into a fielder's choice and Ben Revere flew out to end the inning.
"We just can't come up with a bit hit right now, probably because their pitching staff is throwing the ball pretty good," Gardenhire said.
The White Sox, meanwhile, added much-needed insurance runs on an RBI single by Paul Konerko in the seventh and Beckham's RBI single in the eighth.
"Those are what you need right at the end because the Twins aren't going to be giving up any time soon," White Sox manager Robin Ventura said. "It's one of those you know they are going to keep coming. Getting those runs late is big."
Morneau added an RBI single in the eighth but that was it as Chicago beat the Twins for the 10th time this season to clinch only the team's second season series victory against Minnesota in the last 12 years.
And although the Twins also fell a season-high-tying 25 games under .500, Monday was a memorable day for the 38-year-old Carroll.
"[10 years is] a goal when you make it to this level you try to reach and, fortunately, I was able to do it. It's a proud moment in my family," said Carroll, whose wife, kids, bothers and father were at the game. "It's not fun to lose and go home with a loss, but in time I'll be able to look back and understand and appreciate what this day is about."