With the bases loaded, Youkilis produced his game-turning homer in the fifth inning after the teams had been level-pegging at 2-2.
The White Sox remain top of the American League Central, two games ahead of the Detroit Tigers, who were 5-3 winners against the Toronto Blue Jays.
The Yankees continue to head the AL East by four games from the Tampa Bay Rays, who were edged out 1-0 in the 10th inning by the Kansas City Royals, Eric Hosmer with the decisive two-out single.
Tracking the Rays are the Baltimore Orioles who stand just a game further back after a 5-3 success against the Texas Rangers, sparked by a two-run homer from Nate McLouth.
Jesus Montero struck a three-run homer as the AL West's bottom side Seattle Mariners made it seven wins in a row, with a 5-1 success against the slumping Cleveland Indians who in turn fell to a seventh successive defeat.
The Los Angeles Angels overcame the Boston Red Sox 5-3, and the Oakland Athletics were 4-1 winners over the Minnesota Twins on a successful return for left-handed pitcher Brett Anderson.
Battling for supremacy at the top of National League West are the San Francisco Giants and the Los Angeles Dodgers.
It was the Giants' night in Los Angeles as they recorded a 4-1 victory to extend their lead to one-and-a-half games.
No team has a better record this season than the NL East-leading Washington Nationals, and they improved their win-loss to 77-46 by overcoming the Atlanta Braves 4-1, helped by home runs from Ian Desmond and Jesus Flores.
NL Central front-runners the Cincinnati Reds edged out the Philadelphia Phillies 5-4, Zack Cozart with the decisive homer in the ninth inning, while Chase Headley hit a 10th-inning two-run homer as the San Diego Padres defeated the Pittsburgh Pirates 7-5.
The St Louis Cardinals shut out the Houston Astros 7-0, the Milwaukee Brewers beat the Chicago Cubs 5-2, while the Colorado Rockies battled to a third win in a row, 6-2 on the road against the New York Mets.
From 5-0 behind, the Miami Marlins recovered to squeeze a 6-5 win after 10 innings against the Arizona Diamondbacks.