Quintana, who entered his start against the Kansas City Royals still searching for his first victory, implored Renteria to allow him to go back out for the seventh inning after he had already struck out 10 hitters.
Renteria struck a deal with his starter: If the game was still tied, he could continue his outing. If not, he would turn the game over to the White Sox bullpen.
Avisail Garcia ended up casting the deciding vote.
Garcia hit a two-run, go-ahead home run and Quintana picked up the victory as the White Sox completed a three-game sweep of the Royals and won their fourth straight game with a 5-2 victory.
Quintana snapped a personal four-game losing streak and allowed only one earned run and scattered five hits over six innings. The outing marked the eighth time in his career that Quintana (1-4) has struck out at least 10 hitters as the Royals dropped their seventh straight game.
"We haven't scored a whole lot of runs for (Quintana) and he went after (the Royals), he attacked the zone," Renteria said. "It was great for him to get the win."
Garcia snapped a 2-2 tie in the sixth with a two-run homer after the Royals tied the game in the top half of the inning. Garcia's shot came with two outs and after Royals starter Nate Karns got back-to-back groundouts following Melky Cabrera's leadoff single.
Leury Garcia added a solo home run in the seventh inning to pad Chicago's lead. The White Sox bullpen made it stand up before David Robertson earned his fifth save. But it was Quintana who laid the groundwork.
After not receiving a lot of run support in his first four starts, the early two runs provided Quintana with an extra dose of confidence. He kept Royals hitters guessing throughout the day and finally got his first victory after much anticipation.
"It was a mission," Quintana said. "Everybody was doing their job. I needed this outing, so I felt really good on the mound. It was extra motivation to win my first one. (White Sox catcher Geovany) Soto called a good game, and we focused the whole game. I threw the ball well."
The White Sox scored two first-inning runs to jump out to an early lead. Jose Abreu and Todd Frazier collected back-to-back RBI doubles. Abreu's double scored Tyler Saladino, who singled earlier in the inning.
The Royals responded with single runs in the fifth and sixth innings to draw even with the White Sox. Jorge Bonifacio delivered an RBI single in the fifth, which scored Alcides Escobar. The run was not charged to Quintana however, as Cheslor Cuthbert reached on an error by Abreu.
Escobar tied the game at two in the sixth inning with a RBI groundout as the Royals' offense continued to struggle. But after making solid contact throughout the day, Kansas City manager Ned Yost said he was encouraged by what he saw despite the result.
"We hit the ball right on the screws -- we just couldn't find any holes," Yost said. "... Offensively, there were good signs today and I think that bodes well going into the off-day and the pitching has been pretty solid. So hopefully, good things happen when we get home."
As the Royals look to rebound, Quintana hopes to build off Wednesday's victory.
"I needed that win," Quintana said. "I never started like that (with four straight losses), so I'm really proud of the first win for me. The first of many, so I can't wait to keep doing my job."
NOTES: White Sox 1B Jose Abreu left Wednesday's game with a minor right hip flexor strain. Abreu was injured when he attempted to back-hand a ground ball in the top of the fifth inning. Abreu, who doubled in his first two at-bats, is day-to-day and will be re-evaluated Friday. ... For the second straight day, Royals DH Mike Moustakas hit in the leadoff spot and CF Lorenzo Cain took over the No. 2 slot a day after the Royals scored five runs -- their highest offensive output since April 14. "We're just trying to create some offense," manager Ned Yost said. ... White Sox RHP James Shields (strained lat muscle) is expected to start throwing in the next day or two, manager Rick Renteria said Wednesday. Shields was placed on the 10-day disabled list and replaced in the rotation by RHP Mike Pelfrey, who will start Friday in Detroit against the Tigers.