DETROIT — This Goliath-turned-David tale was expiring more quickly than Ben Carson’s popularity Saturday afternoon at Comerica Park. Two Tigers had scored already, three more stood on base, and how in the heck was CC Sabathia going to get out of this fourth-inning frozen mess?

Behind the safety of a heated suite, surrounded by 17 family members and friends who flew in for this game, Amber Sabathia watched her husband prepare for this critical moment, and she believed.

“CC does very well in those situations,” the big lefty’s wife said afterward. “It seems like when it’s pressure, it seems like when it’s on the line, when it could be a game-deciding hit, he does good and he pulls through. And he did of course today. Let’s hope it goes like that the rest of the season.”

The term “pulling through” carries a new connotation for the Yankees’ beloved veteran southpaw. He escaped the fourth when Brett Gardner tracked down Mike Aviles’ blast to the left-field warning track, and he went on to win his first start of 2016, 8-4 over the dangerous Tigers in what the home team called the coldest game in its stadium’s 16-year history (first-pitch temperature of 31 degrees).

Yet this marked a far greater point of demarcation for Sabathia than just the beginning of a new season. The 35-year-old prevailed in his first start as a recovering alcoholic, after leaving the Yankees to undergo treatment last October.

“It definitely feels good,” Sabathia said. “Just to be pitching in a big-league game, be on a big-league mound and for us to come out with the win. So that’s good.”

“It’s almost like starting over again,” Amber Sabathia said. “He had — not so much to prove himself — but it’s a big year for him. And he knows that, too. It’s exciting.”

The Tigers fielded a lineup with eight righty hitters (including switch-hitter Victor Martinez). Last year, righties hit .309/.363/.502 against Sabathia and lefties .186/.237/.279. Given Sabathia’s struggles since 2013, and that the Yankees didn’t guarantee him a spot in their starting rotation until the day they packed up and left spring training, extreme confidence could not have existed inside the visiting clubhouse.

Nevertheless, in conditions that Sabathia said “sucked,” he went through the lineup perfectly through one turn, and his teammates knocked around former Met Mike Pelfrey in his Tigers debut, lighting up Big Pelf for six runs in 3 2/3 innings. Sabathia survived not only his fourth-inning adversity but also the fifth, in which the first two batters reached base — he induced Justin Upton to hit into a 1-4-3 double play — and he wound up being the first Yankees starting pitcher this season to get through the sixth inning as he allowed three runs and four hits, walking four and striking out three.

“It’s really good, and on a day where we needed some innings,” manager Joe Girardi said.

It was Girardi who received Sabathia in his office last Oct. 4, the last game of the regular season, and blessed the pitcher’s request to leave the team before the postseason and get help for his alcoholism. Girardi said he appreciated that Saturday’s game had more to do with than just the AL East standings.

“I think it’s big for him,” Girardi said. “With what he went through, and having to walk away when he did, I know it was very difficult on him. But I really believe he made the right decision. His health and his family’s well-being obviously take precedence over this. And to be able to come and win the game today, six months later, I think it’s really important to him.”

His cellphone blew up with far more text messages than usual, Sabathia said, both before and after his start. He saluted Amber and his mother, Margie, for being there “every step of the way. Obviously, these guys in here were great. But my mom and my wife were just kind of that rock for me during that tough time. It’ll be good to see them tonight and go to dinner.”

This season won’t be easy for Sabathia or the Yankees. Nevertheless, he will keep working to pull through. You never doubt that about him.