"You've got guys in scoring position and a walk doesn't really help much," Bradley said. "I definitely wanted to make him throw a strike after walking the previous batter and I was able to get in a great count and put a good swing on it."
With the score tied at 4 after 13 innings, the White Sox ran out of pitchers after Daniel Webb threw 59 pitches in three innings, so manager Robin Ventura turned to Garcia (0-1) to start the 14th. Garcia is the first White Sox position player to take the mound since Casper Wells pitched a scoreless inning last June.
"We just, for one reason or another, we didn't seem to throw it over," Ventura said. "So, you know, a game that if you are going to give them that many opportunities, you are little surprised you are in it that late into the game.
"Once it starts going a little bit later, you sniff around at guys that can pitch. And there were a lot of takers. But he got the nod."
Chris Capuano (1-0) pitched 2 2/3 innings of scoreless relief to get the win. Burke Badenhop got the final out for his first save of the season.
Each team blew a lead in the ninth inning or later.
The Red Sox managed just six hits, but took advantage of the 15 walks issued by Chicago pitching, including 11 after the seventh inning.
The White Sox have had a strong start to the season in every area except the bullpen. Before Wednesday's struggles, Chicago relievers had allowed 29 earned runs in 40 innings pitched for an ERA of 6.53.
In scoring twice in the eighth and ninth innings, Boston had just one hit -- a weak infield single down the third-base line -- but were walked six times in the two innings by White Sox relievers.
Alexei Ramirez hit a two-run homer to extend his hitting streak to begin the season, and John Danks allowed one run in six innings to give White Sox a 3-1 lead after seven innings.
The win snapped a three-game losing streak for the Red Sox.
"Our pitchers did a heck of a job," Boston manager John Farrell said. "Our bullpen came in with no margin for error and put up zeroes. We had multiple opportunities with men on base and we're still grinding away. We took base on balls when they were issued, which was a lot, and I'm thankful we walk away with the win."
White Sox 1B Paul Konerko agreed to come back for one more season knowing he'd be a part-time player, but before Thursday, he had only eight at-bats in six games and started one. He's expected to make his first home start Thursday in the series finale. "I think he's done all right," Ventura said. "It is an adjustment. He's always looking for (pinch-hitting) spots. He's playing along with the game and trying to figure out what's going to be the spot." ... Boston LHP Jon Lester faces LHP Chris Sale in the series finale. ... Red Sox OF Shane Victorino (hamstring) is expected to begin a rehab stint Friday, while RHP Koji Uehara (shoulder) was fine following a bullpen session Wednesday and could be available Thursday.
Copyright by STATS LLC and The Associated Press
CHICAGO, IL - APRIL 16: David Ortiz #34 of the Boston Red Soxhits a single in the 1st inning against the Chicago...
13,302 (32.8% full) - % is based on regular season capacity
46 degrees, partly cloudy
Home Plate - Cory Blaser, First Base - Jim Joyce, Second Base - Doug Eddings, Third Base - Marvin Hudson
Alexei Ramirez is hitting .529 in at-bats ending with a pitch up in the zone or above this season, the fifth-highest rate in MLB. Clay Buchholz has allowed four hits on pitches up in the zone so far this year, but two of those hits were home runs.