The patchwork lineup pieced together a tapestry in the form of a 5-2 victory behind the sturdy Kelvim Escobar and electric Francisco Rodriguez.
The Angels seized the weekend series 2-1 while winning consecutive road games for the first time this season.
"That was a very important game for us," said Izturis, among the most consistent and valuable of Angels through 25 games. "Kelvim gave us a great game, we made the plays we needed and we're going to Kansas City feeling good."
Backed by Izturis and Vlad Guerrero, who homered back-to-back to tie the game in the fourth, Escobar gamely protected a one-run lead provided by Izturis with his RBI single in the fifth after a single and steal by Orlando Cabrera.
After 106 pitches, having walked Ryan Sweeney with two outs in the seventh, Escobar (2-1) turned it over to K-Rod. The closer struck out Darin Erstad on a wicked slider and finished off the Sox in the ninth for his eighth save after Erick Aybar's two-run single in the top of the inning had given him a three-run cushion.
"I had all my pitches working, my whole repertoire -- slider, breaking ball, changeup, split-finger," Escobar said. "But the most important thing was command of my fastball."
Escobar walked one and gave up four hits while striking out three and shaving his ERA to 3.28.
Chicago's Mark Buehrle (2-1) was charged with the loss after lasting six innings and giving up nine of the Angels' 12 hits. Leadoff man Gary Matthews Jr. reached base four times, triggering an offense that produced without Garret Anderson, who is day-to-day with a tight rip hip flexor.
"That was huge, getting some runs for Eskie -- he had a problem last year with run support," said Hillenbrand.
The first baseman, strictly a DH until Sunday, deftly handled a 3-6-3 double play in the sixth inning and watched Wood start a 5-4-3 double play in the seventh. Both corner infielders atoned for errors made earlier in the game that did not have any lasting impact.
"Pitching and defense, that's the name of the game," Escobar said. "The guys behind me made the plays, and it was huge. The double play, that's my best friend.
"The biggest thing is winning the series. If we keep doing that, we'll be in good shape."
The White Sox had struck first against Escobar in the third inning on a two-run homer by the former Angel Erstad.
Manager Mike Scioscia marveled that Escobar had "just a few pitches he'd like back," notably the 3-2 changeup that stayed up in Erstad's hitting zone.
After delivering his RBI single in the fifth for the 3-2 lead, Izturis felt tightness in his right hamstring running the bases, leaving the game -- and second base -- to Aybar.
Aybar's clutch two-out, two-run single left him 7-for-15 (.467) with runners in scoring position. It came against Bobby Jenks, who had just yielded Wood's first Major League hit, a fastball lined to left.
After the game, Wood was returned to Triple-A Salt Lake to clear roster space for Chone Figgins, who comes off the 15-day disabled list after fracturing two fingers on his right hand on March 22.
A beaming Wood was thrilled that his milestone hit (and first run scored) came in front of his parents, an uncle and his girlfriend. The ball, he added, would go to his parents.
"Being able to see how my teammates handle themselves, the intensity of playoff[-type] baseball, that was the big thing," Wood said of his brief introduction to the Major Leagues, which lasted four days. "I got the jitters out of the way, felt the excitement of getting the first hit. ... I've definitely benefited from the experience.
"Figgy's coming up, feeling healthy, and I'm happy for him. [Going down] doesn't really sting as much as how exciting it was for three or four days. It makes you realize how bad you want to be up here."
The Angels lost a run in the seventh on a call by home-plate umpire Adam Dowdy, who ruled that Reggie Willits left third base too soon on Cabrera's fly ball to left, caught with a dive by Ryan Sweeney.
Scioscia protested to no avail before being tossed, his and the team's first ejection of the year. Bench coach Ron Roenicke managed in Scioscia's absence and showed that he could dial the right number -- K-Rod's.