Beckham's solo shot and a two-run blast from Konerko in the first were the only runs allowed by Cubs starter Jeff Samardzija (4-2).
Konerko suffered a laceration above his left eye and swelling when he was hit by a Samardizja pitch in the third inning and had to leave the game. He was to have more tests to determine the extent of the injury.
Wood's impending retirement dominated the pre-game conversations as the right-hander shagged batting practice balls in the outfield with his son. Wood was expected to retire after one more appearance with the Cubs and he made that in the eighth after Samardzija walked Adam Dunn.
Wood, who began his major league career with the Cubs in 1998 and struck out 20 Houston Astros batters in his fifth major league start, took the mound to rousing cheers. When Wood struck out Dayan Viciedo -- the only batter he faced -- he was taken out as teammates congratulated him on the mound and Dunn doffed his batting helmet and clapped from first base.
Wood left to a rousing standing ovation and was hugged by his son as he reached the dugout. Moments later, Wood emerged for a curtain call, waving his cap to the fans at Wrigley Field as James Russell threw warmup pitches.
Konerko's 19th career homer in 66 games against the Cubs came one out after a first-inning single by Beckham and made it 2-0.
But the Cubs responded right away against Phil Humber. David DeJesus led off with a fly ball double into the ivy in left field and Tony Campana had a bunt single when Humber slipped down trying to field it. Campana then stole second before Starlin Castro's long sacrifice fly made it 2-1 and sent Campana to third. Humber then struck out Bryan LaHair and got Alfonso Soriano to fly out.
Samardizja hit Konerko with a high tight pitch in the third, sending him sprawling into the dirt and eventually out of the game holding a towel to his face. The next inning, Humber threw a pitch high and behind Cubs cleanup hitter Bryan LaHair in the fourth and home plate umpire Tim Timmons issued a warning to both teams.
The Cubs tied the game in the seventh when Ian Stewart led off with a single and one out later Darwin Barney doubled into the left field corner to finish Humber after just 66 pitches. Matt Thornton (2-3) came in and Samardzija promptly bounced his first pitch through the left side for an RBI single to tie the game and put runners at first and third. DeJesus popped out and so did Campana on a bunt attempt, ending the inning.
Samardzija allowed six hits and three runs in 7 1-3 innings with two walks and eight strikeouts.
Humber allowed five hits and the two runs in 6 1-3 innings and is now 0-2 with three no-decisions since pitching a perfect game against Seattle on April 21. Addison Reed got his fourth save in as many chances with a scoreless ninth that included a double by Barney when White Sox right fielder Alex Rios lost his two-out fly ball in the sun.
Cubs manager Dale Sveum was ejected in the fifth inning after arguing a call at second base with umpire Marty Foster, who was covering second on the play. DeJesus had hit a ball to left center and appeared to be safe at second but when Beckham went to make a tag he knocked DeJesus off the bag and Foster called him out.
Notes: White Sox 3B Brent Morel was a late scratch with a sore back that has bothered him off and on this season. He was replaced by Eduardo Escobar ... Cubs C Geovany Soto will have surgery on a torn meniscus in his left knee and will miss three to four weeks ... The Cubs called up catcher Blake Lalli and optioned out struggling right-hander Chris Volstad, who had an 0-6 record.