It was Chicago's first Cactus League victory, and snapped Texas' two-game winning streak.
Dunn -- who signed a four-year, $56 million contract with the White Sox before the 2011 season, then hit a dismal .159 with just 11 home runs and and 177 strikeouts -- was 2-for-3 and drove in four of Chicago's six runs.
Brent Morel singled and Dayan Viciedo doubled off Feliz in the first before Dunn crushed a 1-2 fastball onto the concourse in right field for an early 3-0 lead. Feliz bounced back to strike out the last two batters of the first, throwing 28 pitches in the frame.
Feliz needed just eight pitches to work through the second, retiring the White Sox in order, before calling it a day. Chicago starter Hector Santiago pitched two scoreless innings, striking out three and walking one. He threw 45 pitches, 25 for strikes.
"I'm not really focused on what happened today," Feliz said. "Obviously, [Dunn] got a hold of one. I'm just working on making my pitches, locating them where I want them, keeping the ball low. I'm just going to be focused on my goal and not going to worry about today too much.
"In the second inning, I came out trying to attack the zone and keep the ball low, and I was more successful in the second inning than the first."
Dunn also connected on a two-out double off Texas' Michael Kirkman in the third, plating Morel for Chicago's fourth run. Morel was 2-for-3 with two runs.
The next inning, Gordon Beckham added a two-run homer off Kirkman to run the lead to 6-0. Texas loaded the bases in the fourth against Chicago's Gregory Infante, but managed just one run on an infield grounder.
Rangers up next: Texas welcomes the Dodgers to Surprise Stadium on Friday at 2:05 p.m. CT, with Rangers left-hander Martin Perez set to take on 2011 National League Cy Young Award winner Clayton Kershaw. It will be Kershaw's Cactus League debut. Two of the Rangers' top relievers -- right-handers Mike Adams and Koji Uehara -- are expected to pitch in the matinee.
White Sox up next: The first of eight games to be played between the Cubs and White Sox during Spring Training and the regular season takes place on Friday at 2:05 p.m. CT at Camelback Ranch, with the game also being televised by WGN and broadcast by White Sox flagship station WSCR-AM. The two teams meet six times during Interleague Play, and the White Sox travel to Mesa on March 18. Chris Sale gets the start, marking his first official trip to the mound as part of the rotation, although he did pitch during an Intrasquad game. Look for Nestor Molina to get back out on the mound after Monday's rough Cactus League debut against the Dodgers.