Flowers' first career multi-homer game lifted Chicago to a 6-3 win over the Minnesota Twins in 10 innings on Tuesday night.
Viciedo broke a 3-all tie in the 10th with a solo homer off reliever Lester Oliveros (0-1). Flowers followed with his second two-run shot of the night later in the inning as the White Sox won for just the fourth time in their last 14 games.
''It's just nice to see, especially with Jose being out tonight,'' White Sox manager Robin Ventura said. ''You get some guys to pick him up and score some runs with some homers.''
After rookie slugger Kennys Vargas gave Minnesota a 2-0 lead in the first with a 423-foot homer, Flowers tied it in the second with his first longball of the night.
About a year removed from major shoulder surgery, Flowers has 12 home runs and is setting the tone for a slew of new arrivals as the White Sox battle the Twins to stay out of last place in the AL Central.
''Even though we're not where we want to be right now, there's still a level of professionalism you have to keep,'' Flowers said. ''Trying to get them off on the right foot, doing the right things.''
Carlos Sanchez added three hits, including an RBI double that gave Chicago a 3-2 lead in the second.
An errant pickoff attempt allowed pinch-runner Aaron Hicks to advance to third base in the ninth, but Daniel Webb (6-4) recovered and got Kurt Suzuki to fly to right and end the inning.
Jake Petricka pitched the 10th for his 11th save in 14 chances.
Danny Santana lined a double just over the glove of left-fielder Michael Taylor in the second to score Eduardo Escobar and tie the game at 3.
Given a 2-0 lead in the first, Twins starter Tommy Milone couldn't hold it and was removed after walking four and allowing three runs in 3 2/3 innings.
''Just falling behind hitters. I need to get back to attacking, attacking the zone, staying low, just being aggressive,'' Milone said.
Since joining the Twins via trade in July, Milone has a 7.84 ERA in five starts.
After a rough first couple of innings, Chicago starter Hector Noesi settled in and allowed three runs over seven innings, buying the White Sox enough time to power their way back into it.
''Noesi settled down after the first couple innings,'' Flowers said. ''Started getting better location. We were able to do a lot more.''
White Sox CF Adam Eaton received his first career ejection when home plate umpire Greg Gibson quietly tossed him between the sixth and seventh innings after Eaton struck out.
''I had one, one-liner and maybe another line and he had enough apparently,'' Eaton said. ''I didn't even know I got thrown out. I was grabbing my glove.''
RODON NOT CALLED UP
Chicago called up seven players before Tuesday's game, but not top prospect Carlos Rodon, the No. 3 overall pick in the 2014 draft. Rodon, a left-hander, had advanced all the way from rookie ball to Triple-A Charlotte since getting drafted in June.
Twins SS Eduardo Escobar couldn't shoo away a large flying insect that was hovering around his helmet during an at-bat in the fourth. It eventually landed on his neck and had to be plucked off by Gibson.
TWINS: Add SS Nick Gordon to the list of Twins' top prospects to end their 2014 season injured. Gordon, the fifth overall pick in the 2014 draft, broke his left index finger and will miss the postseason for Elizabethton, Minnesota's rookie ball affiliate.
Gordon joins CF Byron Buxton (concussion), 3B Miguel Sano (elbow), P Alex Myer (shoulder) and P Kohl Stewart (shoulder) to wind up missing the end of the 2014 with injuries.
WHITE SOX: Abreu sat out with general soreness. Ventura hopes to have the rookie slugger back Wednesday.
Trevor May (0-4, 10.42 ERA) has walked 14 batters in his first 19 major-league innings for the Twins. He'll try to turn it around against LHP John Danks (9-9, 4.88) when this two-game series concludes on Wednesday night.