Alberto Callaspo set up the blast by lining a double into right-center field with one out.
The Royals took the series, two games to one, as 18,091 fans watched the finale at U.S. Cellular Field. The Royals scored just six runs in the tight-knit series but made them count.
Crisp was ready when Jenks, the White Sox premier closer, came in with a fastball.
"He's one of the best pitchers in the game," Crisp said. "I swung at the first pitch so he wouldn't get ahead of me. I was looking for the fastball, but I was actually looking away. I just really reacted, and that's what happens when you let your reactions work for you -- good things happen."
Crisp, a switch-hitter, was batting left-handed against Jenks and pulled the pitch over the Bullpen Sports Bar in right.
"He tried to sneak a fastball in there and Coco was ready for it," said Royals manager Trey Hillman. "It's good to see."
Not for Jenks, who tried to explain.
"A cutter that didn't cut," Jenks said. "It happens from time to time. After what we've been doing to him all series and what I did to him in the first game, he was looking in, and the pitch location was in, but it didn't cut like I wanted it to off the plate."
Kyle Davies, extending his superb 2008 September and 2009 Spring Training, pitched seven shutout innings against the White Sox. He gave up just three singles and matched his career best with eight strikeouts.
But he left with the score 0-0 because the Royals couldn't penetrate the White Sox pitchers either. So Davies went away with no reward for his effort.
"You know what, the team got the reward for that," Davies said. "The whole team played great -- like it was the playoffs, even though it was just the third game of the year."
Ron Mahay relieved Davies at the top of the eighth and got through a scoreless inning.
Joakim Soria came on to pitch the ninth and gave up a leadoff double to Carlos Quentin, his first hit of the season. Quentin took third as Jim Thome rolled out and scored when Jermaine Dye grounded out to short.
There was a white-knuckle finish as Paul Konerko walked on four pitches and third baseman Alex Gordon booted Alexei Ramirez's hopper for an error. But Soria notched his second save by striking out pinch-hitter Wilson Betemit.
"He's a great hitter, too," Soria said, "and as a pinch-hitter, he does well."
Not this time.
Davies got some defensive help from left fielder David DeJesus, who took an extra-base hit away from Dye in the Sox second with a headlong catch in left center.
This series was marked by excellent starting pitching.
"You can't have six starting pitchers go out there and do it better for their teams than they did in this series," Hillman said.
Against Thursday's White Sox starter, lefty John Danks, the Royals got their first hit on John Buck's no-play trickler down the third-base line in the third. After an out, Crisp walked and DeJesus singled to load the bases, but Mark Teahen lined sharply into a double play.
Jose Guillen, after drawing a walk to start the sixth, tried to spark something with a stolen base -- just his third in two years -- with one out. But Gordon and Mike Aviles each flied out.
That completed six scoreless innings for Danks, and his day. He gave up just three hits along with three walks. Mike MacDougal relieved him in the seventh.
The Royals had another chance with one out in the seventh when pinch-hitter Callaspo singled and Crisp doubled into right center, putting runners at second and third. But lefty Matt Thornton replaced MacDougal and got DeJesus to roll out meekly and fanned Teahen.
Guillen led off the eighth with a single against righty Octavio Dotel, but he was stuck at first base as pinch-hitter Mike Jacobs, Gordon and Aviles all struck out.
But with Crisp's clutch blast, the Royals go home to Kansas City to re-open the new-look Kauffman Stadium with a winning record.
Maybe it's a new-look team as well.