Ronald Belisario allowed a two-out RBI single to Suzuki before Donnie Veal retired Joe Mauer on a grounder.
Matt Lindstrom came on in the ninth after being announced as the closer by Ventura before the game. The right-hander gave up a one-out double to Chris Colabello before striking out Trevor Plouffe and retiring Arcia on a grounder to the mound for his first save since April 2011 when he was with Colorado.
Nolasco took the loss in a shaky debut with Minnesota. One of the top free agent pitchers last winter, he gave up five runs and 10 hits in six innings.
"I thought we played good, we battled all game," Nolasco said. "Put up some runs, gave a good fight to Chris Sale and made it interesting late. Come back tomorrow or the next day and try and build off that."
The Twins are trying to pick themselves up after back-to-back 96-loss seasons and dropping a staggering 291 games the past three years.
There was a glitch before the game with the Twins' replay system as two blown fuses disabled a pair of monitors in the Minnesota clubhouse. That was fixed in time for the first pitch, but things didn't get much better for the Twins.
That is because the White Sox got the big hits from Abreu and De Aza to back Sale.
Notes: Konerko had started the previous 15 openers for the White Sox and 16 straight overall. He is in a reduced role after re-signing for one year. ... Minnesota LHP Brian Duensing was placed on the paternity list before Monday's game. RHP Michael Tonkin was recalled from Triple-A Rochester to replace Duensing, whose wife Lisa gave birth to a boy named Boston Matthew Duensing. . Twins general manager Terry Ryan didn't travel with the team to Chicago. Ryan was undergoing radiation to treat cancer.