Clinging to a one-run lead with no room for error, he found a way to close it out.
"A game like that, just got to buckle down and keep fighting," Wilhelmsen said. "We can't lose that game."
Dewayne Wise hit a two-out RBI single to get the White Sox within one before Wilhelmsen issued his third walk of the inning, to Alexei Ramirez. That brought Flowers to the plate with three runners on, but Wilhelmsen managed to throw three straight strikes with the game in the balance.
"He just bowed his neck, man. That's what you have to do," Mariners manager Eric Wedge said. "That's why he's our closer is because he's tough. He didn't give in to it. I mean, he didn't tighten up. You still saw the ball jumping out of his hand."
Gutierrez sparked the winning rally when he led off with an infield single. He advanced on Michael Saunders' sacrifice and came home when Kendrys Morales drove the next pitch down the first-base line.
Jesus Montero then singled home pinch runner Robert Andino as Seattle earned its fourth win in its past 20 games in Chicago dating to the 2008 season. The Mariners have only 11 wins in their past 44 games against the White Sox overall.
"We don't look at that. We've got a completely different cast of characters here," Wedge said. "I guarantee none of them know that. What we're trying to do is win series, and you get that first win of a series and it goes a long way heading in the right direction."
Kameron Loe (1-0) pitched a perfect ninth for the win.
Alejandro De Aza and Alex Rios homered for Chicago, which went 8-1 against Seattle last season. Paul Konerko had an RBI single in the fourth for his 2,137th hit with the White Sox, passing Frank Thomas for third on the franchise list.
"We scored some runs and battled back into it on a tough, cold night, but a loss is a loss," Konerko said. "We have to realize there's a lot of good teams in this league and one inning can do the game in, so you've really got to stay on your toes out there."
The White Sox were hurt by pitcher Jose Quintana's costly error that paved the way for Seattle's five-run fifth inning. With none out and a runner on second, Dustin Ackley hit a grounder to first and Quintana hustled over to cover the bag. The throw from Konerko was a little behind him, but the left-hander tried to grab it with his bare hand and it squirted away.
"I felt that changed the inning for me," Quintana said through a translator. "It kind of took the wrong way for me with that error."
The Mariners then strung together five consecutive hits to chase Quintana and open a 6-1 lead. Gutierrez had a two-run double and scored on Saunders' triple. Morales added an RBI single, stopping a 1-for-14 slide.
But the White Sox responded with four runs in the bottom half and another in the seventh. De Aza hit a two-run shot and Rios had a solo drive in the fifth, and Rios' grounder brought home Gordon Beckham with the tying run two innings later.
"The good part about tonight is it's over, basically," White Sox slugger Adam Dunn said. "It was miserable out there for everybody. We had our chances, and it didn't happen. We'll come out tomorrow and hopefully get 'em."
Gutierrez got the Mariners off to a nice start when he drove Quintana's fourth pitch just over the wall in the right-field corner. It was Gutierrez's second leadoff homer of the season and No. 3 for his career.
"Just trying to get on base. That's it," Gutierrez said. "Obviously in the leadoff spot, when the game starts, they throw more fastballs, so I'm trying to be ready for that. If I hit it good, it can go out."
The game-time temperature was 34 degrees. ... Mariners ace Felix Hernandez will make his second start Saturday. The right-hander gave up three hits over 7 2/3 innings in a 2-0 win at Oakland on Opening Day. He will be opposed by RHP Dylan Axelrod, who will be making his season debut. ... With the short turnaround between games, Konerko likely will get a day off Saturday. Chicago manager Robin Ventura also said C Hector Gimenez probably will play. ... Wedge said C Kelly Shoppach likely will be in the lineup Saturday.