Semien hit a three-run drive as part of a five-run second inning. Konerko added a two-run shot to back Erik Johnson, who allowed three runs and four hits over six innings in his final start of the spring. Johnson struck out four and walked three.
Cano went 2 for 4 with a three-run double in the seventh. After bolting the Yankees for a $240 million, 10-year contract with Seattle, the All-Star second baseman is batting .465 this spring.
"He turned it up a little bit with the bases loaded," Mariners manager Lloyd McClendon said. "Really got his hands in nicely and put a nice swing on it."
The 23-year-old Semien, who showed promise during a September call-up last season, has a major league roster spot all but clinched. He could start the season opener at second base if Gordon Beckham isn't ready due to injury.
"My goal in the offseason was to make the team," Semien said.
The White Sox put together five consecutive hits off starter Blake Beavan in the second. A two-base error by right fielder Michael Saunders opened the door for Chicago, as Konerko scored the first run. Alexei Ramirez drove in a run with a single, Tyler Flowers singled and Semien cleared the bases.
Seattle trailed 7-3 in the seventh, but Mike Zunino's single and back-to-back walks issued by reliever Donnie Veal brought up Cano with the bases loaded. Cano doubled before Veal retired the next three hitters.
Mariners reliever Charlie Furbush struck out all four batters he faced.
White Sox: Johnson is ticketed for the big league rotation, which could be set as soon as Tuesday. He threw 94 pitches.
"Today was a good one to end on and another good one to build off of," he said.
Mariners: Beavan was having a solid spring until his last two outings. He lasted 5 1/3 innings Monday and gave up seven runs on seven hits without a walk, striking out three. He also allowed seven earned runs in his previous start, and might now be on the outside looking in at a spot in the unsettled rotation.
"I need to make better pitches when I'm ahead. Five of those hits they got were 1-2, 0-2 pitches," Beavan said. "I'm prepared for whatever decision they make."
Beavan's chances might have improved, however, when the Mariners released Scott Baker on Monday. The 32-year-old right-hander asked for his release after refusing an assignment to Triple-A Tacoma.
Baker was 1-1 with a 6.75 ERA in four spring training starts.
ACKLEY KEEPS HITTING
Dustin Ackley's double gave him a team-high seven this spring, and he also leads the Mariners in hits with 24 and RBIs with 14. The left fielder is batting .414.
Konerko, the White Sox designated hitter, hit his first home run of spring training in the sixth. He finished 2 for 3 but has just two extra-base hits in 39 at-bats.
White Sox: First baseman Jose Abreu returned from having the weekend off due to a sore right ankle. He went 0 for 3 and committed an error, though he made a couple of good defensive plays.
Beckham remains shut down from baseball activity due to a strained left oblique.
Mariners: Hisashi Iwakuma played catch for a few minutes, throwing a baseball for the first time this spring. He's moving closer to returning from a middle finger injury, but won't open the season in the rotation.
Taijuan Walker will pitch three innings in a minor league game Tuesday, trying to get back soon from shoulder soreness.
White Sox: Opening day starter Chris Sale makes his final start Tuesday before the season begins, against Colorado in Glendale. It will be his fifth outing of the spring.
Mariners: Felix Hernandez on Tuesday makes his fourth and final start before the season opener. He will face Kansas City in Surprise.