The next inning Beckham fouled off three pitches before hitting a high fly that just reached the section of Wrigley Field's left field stands that jut in. It was his third home run of the year.
Samardzija (4-2) took the loss after giving up seven hits and all three runs over 7 1/3 innings. He walked two and struck out eight.
He was lifted after walking Adam Dunn in the eighth and Kerry Wood came in and struck out Dayan Viciedo. Wood earlier let it be known he planned to retire as a player after a final appearance. He left the field to a standing ovation.
Matt Thornton (2-3), who allowed the single to Samardzija and got two outs on three pitches, collected the win. Addison Reed pitched the ninth in earning his fourth save.
Beckham singled with one out in the first and, an out later, Konerko hit a smash deep into the left-field stands for his 10th home run of the season. Konerko was hit by a pitch near his left eye his next time up and left the game.
The Cubs got a double by David DeJesus, a single from Tony Campana and a sacrifice fly from Starlin Castro in their first three batters but only managed one more hit off White Sox starter Philip Humber until the seventh.
Ian Stewart singled and took third on a Darwin Bradley double when Samardzija greeted Thornton with a single through the left side. It was Samardzija's first hit of the season.