It was also the first time the Rangers had been swept in a series of three or more games since June 14-16, 2011, at New York against the Yankees. The loss snapped Texas' streak of 52 straight series of three or more games without being swept, which was the longest active streak in the Majors.
The Rangers had lost both games of a two-game set to Kansas City on May 14 and 15 this season.
Texas opened the series on Tuesday by getting blown out, 19-2, before falling, 5-4, on Wednesday night and dropping another one-run game in the finale.
"They played real good baseball the three days here and we just didn't score enough runs, and they did," Rangers manager Ron Washington said. "We pitched well, except for the first night, but tip your hat. They're playing well and they're swinging the bats well, and they've certainly always had good pitching. It just showed up against us this series, as far as putting runs on the board goes."
All-Star left-hander Matt Harrison, who fell to 11-4 but lowered his ERA to 3.10, took the loss, allowing two runs on eight hits in eight innings. The American League Pitcher of the Month for June saw his seven-game winning streak snapped despite tossing his second complete game of the season.
Rangers starters have thrown five complete games this season, but the club is only 2-3 in those games.
"He continued to do what he's been doing all year to this point -- pitch well," Washington said. "It was a 2-1 ballgame. Usually when the other team scores two runs, we figure we have a chance to win that game."
Youkilis' solo homer, an opposite-field shot on a 1-1 sinker, was the first home run Harrison gave up in five starts and snapped a streak of 43 1/3 consecutive homerless innings for the lefty.
"You just want to go up and have good at-bats," Youkilis said. "Some days it's going to be a good hit and some days it's not going to matter. You want to have good hits all the time, but sometimes it works where it's a clutch hit and sometimes its early in the game. The clutch hit is magnified more."
Harrison, who struck out five batters and walked two, was more upset with his leadoff walk to Youkilis in the bottom of the fourth after the Rangers had taken a 1-0 lead in the top of the inning. After the walk, Harrison allowed back-to-back singles to Paul Konerko and Alex Rios to load the bases before Youkilis scored on a groundout by Alexei Ramirez.
"I was definitely pretty upset [in the fourth] when we scored in the top of the inning and I walked the leadoff guy and ended up giving them the run back," Harrison said. "That tied the game back up, put the momentum back on their side."
Youkilis' homer was more than enough for White Sox starter Jose Quintana. The left-hander, who improved to 4-1 with a 2.04 ERA, held the Rangers to two hits and struck out a career-high eight while tossing eight innings of one-run ball.
The eight innings tied a career high for Quintana, who is 2-0 with a 2.04 ERA over his last five starts.
"He's doing great" Konerko said. "If you're going to beat him, you're really going to have to string some hits together. And he doesn't walk a lot of guys, either, so it seems like you have to string some hits against him, and that's tough to do."
The Rangers' lone run came in the fourth inning, when Quintana issued a leadoff walk to second baseman Ian Kinsler. Kinsler advanced to second on a groundout, then scored when Adrian Beltre's comebacker ricocheted off Quintana and into shallow right field.
Beltre's knock was the last hit allowed by Quintana, whose win was preserved by Addison Reed with a perfect ninth inning.
"Other than that first game, I thought we played pretty good baseball; we just didn't put enough runs on the board," Washington said. "I do think if you go check, they've lost three in a row before. I think if you go check, a lot of teams in the American League have lost three in a row. We'll be fine."