OAKLAND, Calif. (AP) - The White Sox head back to the Windy City from a solid road trip with a pair of milestones to celebrate alongside their home fans.

They nearly had one more win to take along, too.

With two of the American League's top pitching teams dueling it out for a third straight day, Kila Ka'aihue blooped a winning single in the 14th inning soon after Yoenis Cespedes' tying two-run homer, and the Oakland Athletics rallied past the White Sox 5-4 on Wednesday.

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A 4-2 trip will have to do. It featured Phil Humber's perfect game Saturday at Seattle, then Paul Konerko's 400th career home run Wednesday to tie the game in the ninth.

``We had a lot of chances,' Konerko said. ``It was nice to get back in the game and give ourselves a chance at getting the win but it just wasn't in the cards.'

Josh Reddick hit a one-out single in the 14th, then Cespedes delivered his fifth homer of the season against Hector Santiago (0-1) after Chicago took the lead in the top half of the 14th. Ka'aihue came through with the big hit in a game that lasted 3 hours, 56 minutes.

``You relish that, you look forward to it when you're taking your BP and your work,' Ka'aihue said. ``You prepare to get that big hit. You don't work on grounding out and flying out. It wasn't the hardest ball I've hit in my life. It won the game for the team, that's all that counts.'

Jim Miller (1-0) struck out Brent Lillibridge for his first major league win after being called up earlier in the day.

Alexei Ramirez hit a go-ahead two-run double with two outs in the top of the 14th on a day ``Take Me Out to the Ball Game' played twice to go along with a 14th-inning stretch.

After a pair of gems from Chicago starters this trip - Humber pitching the 21st perfecto in major league history, then Jake Peavy's three-hit shutout Monday - this day became about the terrific White Sox bullpen until Oakland finally got to the relievers.

Konerko sent the first pitch from A's closer Grant Balfour onto the left-field steps to start the ninth. Konerko became the fourth player in franchise history to reach the 400- or 500-homer mark while wearing a White Sox uniform, joining Frank Thomas, Jim Thome and Andruw Jones.

``Everybody likes the round numbers,' Konerko said. ``When it comes to that kind of stuff, I think when I'm done playing and look back, that's when it might hit home more. But when you're in the middle of the grind and you're grinding every day and working, you tend not to think about that stuff, and you probably shouldn't.'

It looked like the White Sox would take this one after scoring two unearned runs in the top of the 14th.

But Cespedes showed why the A's gave the prized Cuban defector a $36 million, four-year contract.

``I was lucky enough to hit home runs to decide games. This was not the first time,' Cespedes said of his time growing up in Cuba. ``The team is a very young team, but the way we play together we're going to get very far this season.'

Dayan Viciedo reached on third baseman Eric Sogard's fielding error and Brent Morel sacrificed him to second. Eduardo Escobar flied out and Alejandro De Aza walked before Miller relieved Jerry Blevins to face Ramirez.

The A's saved themselves in the 13th with a two pretty defensive plays. Catcher Kurt Suzuki caught pinch-runner Lillibridge well off second base, then shortstop Cliff Pennington chased down Alex Rios' double that skipped into the Oakland bullpen and made a quick throw to Sogard, who then relayed to Suzuki just in time to get a sliding Gordon Beckham.

Konerko's fourth homer of the year spoiled an impressive A's debut by Jarrod Parker, who struck out five in 6 1-3 innings following his call-up from Triple-A Sacramento.

The 23-year-old Parker, making just his second career start, exhibited the poise and improved command the A's hoped he would after sending him down this spring to work some things out.

Reddick's two-out double to right-center in the sixth brought home speedy leadoff hitter Jemile Weeks, who started the rally with a one-out single. Cespedes followed with an RBI single.

The White Sox responded with Kosuke Fukudome's RBI double in the seventh that Cespedes got his glove on in center but couldn't control, and Rios just beat a late throw home to Suzuki.

But Chicago missed a chance to tie it when Fukudome was caught stealing on a squeeze attempt after Morel couldn't deliver a bunt on a 2-1 count.

``It's like you've seen that hundreds of times, long games and anything happens,' White Sox manager Robin Ventura said.

He knows his team will return home for a seven-game homestand to plenty of fanfare as the Red Sox arrive for four. Humber starts Thursday's series opener.

``It's nice. I don't know how long it lasts,' Ventura said of good feelings still surrounding Humber. ``It was a good bonding thing for the team.'

Home plate umpire Jerry Layne took a foul from Escobar off the left shoulder in the fifth and was briefly examined by the A's training staff before staying in the game. Layne returned to the box and playfully grabbed Escobar's bat and jokingly pretending to swing it.

NOTES: Rios went 3 for 5 with two doubles and an intentional walk a day after having his 11-game hitting streak snapped. ... Chicago starter Chris Sale pitched a career-high eight innings.