Chris Volstad (0-3) gave up Encarnacion’s double, the only batter he faced.
Chicago’s poor pitching and defense spoiled a memorable major league debut for Matt Skole, who homered and singled.
Cleveland rallied three times late in Sunday’s game to beat Houston 10-9 in 14 innings.
The Indians received a boost from Chicago’s defense in Monday’s comeback.
The White Sox committed two errors with Yan Gomes batting in the fifth. Gonzalez dropped a foul popup in front of the White Sox’s dugout. Anderson fielded Gomes’ grounder at shortstop, but his throw to first was in the dirt for another error.
The Indians loaded the bases on a force play, a single and a walk, ending starter Dylan Covey‘s day. Luis Avilan retired Jose Ramirez on a popup.
Volstad entered the game but right fielder Daniel Palka, shaded toward right-center, couldn’t make a sliding catch of Encarnacion’s fly ball that landed near the foul line.
Jace Fry faced Alonso, who doubled to center for a 6-5 lead. Moncada booted Melky Cabrera‘s ground ball to score another run.
Skole, called up from Triple-A Charlotte before the game, started a two-run rally in the second with a single. The left-handed hitting first baseman homered in the fourth, a 418-foot shot into the right-field seats.
Skole, 28, signed as a minor league free agent with the White Sox in January after spending seven seasons in the Washington Nationals organization. He was called up when Matt Davidson went on the 10-day DL with back spasms.
Anderson followed Skole with a homer in the fourth.
White Sox: LHP Carlos Rodon (shoulder) will make his third minor league rehab start Tuesday, pitching for Charlotte at Lehigh Valley. Rodon was hit in the head by a line drive in his previous appearance on May 24, but has been cleared to return.
Indians: LHP Andrew Miller (right knee inflammation) played catch Monday, but no firm plan has been set up for a rehab schedule. He was placed on the DL on May 26.