Paul Konerko hit his 427th home run as a member of the Chicago White Sox on Thursday night.

Could it have been his last?

Konerko smacked a solo shot off Kansas City starter Jeremy Guthrie deep into the seats in left field in his first at-bat of a 3-2 loss to the Royals. But the White Sox, who lost for the 97th time this season, have just three games left.

Then Konerko, who has spent the past 15 seasons on Chicago's South Side, becomes a free agent.

The first baseman has hit only 12 homers this season, his lowest total ever in Chicago. But lately Konerko seems to be getting his swing back.

Still the 37-year-old has been quiet on whether he wants to return, even though he discussed his batting stroke.

"Yeah, I've been better in the at-bats and had some better at-bats," Konerko said. "But nothing I'm crazy about. I'm fighting the fight."

Konerko said homering felt good, even if the prospect of the White Sox reaching 100 losses doesn't.

"When you hit a home run, it's the best feeling," Konerko said. "This year, I've hit a lot of balls hard, but the path was on a line or on the ground.

"These aren't balls I hit any less hard than I did tonight. I attacked that one the right way and to get it in the air and get it going. I just haven't done that a lot this year."

Chicago manager Robin Ventura thinks Konerko is still productive, even if his totals have sagged with the White Sox this season.

"I think there are times he hasn't felt as good as other times," Ventura said. "But every time he goes up there he has a good plan. He's a tough at-bat"

On Thursday the White Sox ran into tough luck, again.

Guthrie (15-12) pitched seven strong innings, and David Lough hit a two-run homer for Kansas City. One day after being eliminated from the postseason, the Royals earned their 84th victory, their most since 1993.

The Royals' 6-0 loss to Seattle on Wednesday, combined with victories from all three teams ahead of them in the AL wild-card standings, officially eliminated them from playoff contention.

"The first time in 20 years we've won this many games, that's pretty good, too," Royals manager Ned Yost said. "We feel like we're right there.

"We've had a great year in terms of experience, tasting what it tastes like to win, what it feels like to be in a playoff chase, to be a playoff contender."

Guthrie became the Royals' third 15-game winner since 1997. He gave up two runs and four hits, striking out four and allowing one walk. Guthrie already surpassed his career best win total when he won his 12th on Aug. 5 against the Twins.

"For me, it's a reflection on the team, " Guthrie said. The bullpen pitched tremendous all season long, especially games I threw in and our offense picked us up great along with the defense."

Adam Dunn hit a solo homer for the White Sox, who have lost 21 of 27. The White Sox are 35 games under .500 (62-97) for the first time since ending the 1970 season 56-106 and must win once in this series to avoid finishing with 100 losses, which would be the fourth-most in franchise history.

White Sox starter Andre Rienzo (2-3) pitched six-plus innings and allowed three runs, two earned, and four hits.

Greg Holland pitched a scoreless ninth for his 46th save in 49 chances as the Royals ended a two-game losing streak. Holland set a franchise record in saves, surpassing Dan Quisenberry (1983) and Jeff Montgomery (1993).

Konerko, who missed Wednesday's game at Cleveland after fouling a pitch off his knee on Tuesday, homered in the second inning.

Trailing 1-0 in the fourth, Lough hit a two-run homer, snapping a streak of 21 scoreless innings for the Royals. The last time the Royals scored was in the 12th inning of a 6-5 victory at Seattle on Monday.

Dunn tied the game in the sixth with a long home run to right. It was his 33rd of the season.

In the seventh inning, Justin Maxwell led off with a single and advanced to second on Lough's bunt, then he came around to score after catcher Bryan Anderson fielded George Kottaras' sacrifice bunt and threw it down the right-field line to give the Royals a 3-2 lead.