Konerko hit a tiebreaking drive in the eighth inning for his major league-best eighth homer and the White Sox beat the Seattle Mariners 3-2 on Sunday to complete a three-game series sweep.
"I think the feeling is any time you can win games where you know everybody is not clicking and it's just not coming easy, you feel like you kind of got away with one," Konerko said. "You're always positive about the next game that that's the game you're going to go out and get 15, 16 hits and score seven, eight runs. So, it's nice to get a win when we're not doing that."
John Danks pitched eight sharp innings for Chicago, allowing two runs and eight hits. Danks (3-0) was coming off a strong eight-inning outing in a victory over Tampa Bay.
"They've got something rolling their way, that's for sure," League said. "Nothing to take away from them because they're great hitters. But when you see three home runs to win the game in three days."
The White Sox are hitting .222 as a team and went 0 for 10 with runners in scoring position on Sunday.
"There's a lot of bad luck right now," said Konerko, who has homered in three straight games. "I see guys hit balls hard. There's a lot of little things that will turn in time. A lot of season to go."
Franklin Gutierrez went deep for the Mariners, who absorbed its first three-game sweep of the season. Seattle came to Chicago winners of seven of eight.
"The bullpen again just made too many mistakes up in the zone," Mariners manager Don Wakamatsu said. "This club has given up seven home runs in this series. A lot of them are because of location."
After striking out the first two batters in the eighth, Danks allowed consecutive singles to Ichiro Suzuki and Chone Figgins, but he ended another strong start by getting Gutierrez to fly out. He has allowed five earned runs in 29 innings this season for a 1.55 ERA.
Danks was visited by manager Ozzie Guillen before Gutierrez's at-bat.
"He came out and said this is my game to lose or win," Danks said. "It was my game, he wasn't going to take me out and I definitely appreciate that and fortunately I was able to get out of that inning."
Jason Vargas allowed two runs and four hits in 6 2/3 innings for Seattle.
Kotchman led off the fifth with a deep fly to center. Rios attempted a running catch on the warning track but was unable to make the catch as the ball bounced off the base of his glove. Kotchman easily reached third for his first triple of the season.
After Byrnes lined out, Adam Moore singled to right to give Seattle a 2-1 lead.
The start of the game was delayed 42 minutes by rain.
Juan Pierre helped the White Sox get off to a fast start in the first. The leadoff man was hit by a pitch and went to second on Gordon Beckham's single. He stole third and scored on Moore's passed ball.
Gutierrez tied it with a fourth-inning drive for his second homer in two games.
Mariners SS Jack Wilson was out of the starting lineup for the second straight game with a thumb injury. OF Milton Bradley missed his fourth straight game with a calf injury. Wakamatsu hopes to get both back for Monday's game in Kansas City. ... Pierzynski is in a 1-for-26 slump.