Davidson's third homer of the year reached the upper deck in right field off Ryan Pressly (0-1), and David Robertson picked up his second save.
Left-hander Dan Jennings (1-0) came in to get the victory in relief as Chicago won its third straight game. Jason Castro gave the Twins the lead in the bottom of the first, but that was all of the scoring the Twins would do after being shut out the rest of the game.
Covey wasn't the only White Sox player to make his big league debut on Friday night.
That's because the White Sox starting outfield will all share the last name for Friday.
Left fielder Willy Garcia was recalled from Triple-A Charlotte to fill in while Melky Cabrera is on paternity leave.
More impressive than the double in his first at-bat was the all-Garcia outfield the White Sox went with on Friday.
The Elias Sports Bureau has confirmed this will indeed be the first time a team started three outfielders with the same last name in major-league history, the Chicago Tribune reported.
Renteria smiled broadly at the possibility of three Garcias in the outfield when the subject was broached Thursday, pounding his fist in a baseball glove and saying it could happen.
Matt Davidson hit an opposite-field home run in the seventh inning to provide the winning margin and rookie starter Dylan Covey was steady in his major league debut.
OUR PICK: Santana threw six scoreless innings with four striekouts and two walks while allowing just two hits to improve to 2-0 in Sunday's win over the White Sox. Brian Dozier and Jorge Polanco had a pair of hits with a double, while Max Kepler hit a double as well with his lone hit of the ball game.
Chicago White Sox, catcher Omar Narvaez, right, returns to his position after a chat with pitcher Jose Quintana who wipes his chin after giving up a walk to the Minnesota Twins to load the bases in the first inning of a baseball game Saturday, April 15, 2017, in Minneapolis. And Todd Frazier, who missed two games in Cleveland with illness, is back in the lineup at designated hitter. The start of the game was delayed by rain, however.