ST. PETERSBURG – The best-case scenario sits directly in front of the Astros. They have a chance to sweep the American League Division Series against the Rays if they can win Monday afternoon’s Game 3 at Tropicana Field and do it without having to use any of their three ace starting pitchers more than once.

Not having to push horses Justin Verlander, Gerrit Cole and Zack Greinke -- who’s lined up to start Game 3 against former Astros postseason hero Charlie Morton -- deep into the series would bode well for the Astros’ chances in the AL Championship Series. A rested-and-ready Verlander and Cole pitching at home next week at Minute Maid Park against the Yankees or Twins (New York leads the series, 2-0) would set the Astros up nicely for a return to the World Series.

This isn’t lost on Astros manager AJ Hinch, who gets to hand the ball to Greinke on Monday after Verlander and Cole combined for 23 strikeouts, five hits and 47 swinging strikes over 14 2/3 scoreless innings in the first two games of the series while allowing just two runners reach scoring position. They dominated the Rays and set a high bar for Greinke with a chance to to end the series.

“The biggest value is guys get a day off, too,” Hinch said on Sunday from Tropicana Field. “We would love to be done and close the series out. There’s no reason for us to want to play any more games other than the ones we have to. If you can escape a series without using J.V. and Cole [more than once], that would outstanding, setting up the next series.”

Throughout the Astros’ run to their third consecutive AL West title and a club-record 107 regular-season wins, Hinch has been the picture of focus. Perhaps it’s because he’s managing in his fourth postseason, or he’s putting his Stanford psychology degree to good use. Hinch said when you start wishing something to happen, that’s when it doesn’t.

“That’s why we’re here to win Game 3 and get on to the next series,” he said. “But we’re going to have to play well and play clean like we have. We’ve outplayed them the first couple of games, but not by much. They played very well. We’ve had two elite pitchers pitch tremendously well.”

Since the Astros acquired Greinke and plugged him into the rotation with Verlander and Cole, they are a combined 27-6 in games started by that trio. They are 15-9 in games started by anyone else.

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“I think we’ve got to come out there and try to and find a way to win a game,” Astros third baseman Alex Bregman said. “I think we do that by just taking it pitch by pitch. We’ve got our hands full. Charlie’s good, and they’ve got a great team over there. We’re going to have to play some good baseball.”

Verlander and Cole pitched the Astros’ final two games of the regular season and then one had extra day of rest before taking the mound in the ALDS. Verlander struck out eight batters and allowed one hit in seven innings in Game 1 on Friday, and Cole struck out an Astros postseason-record 15 batters -- the most in a playoff game in 19 years -- and allowed four hits in 7 2/3 innings in a Game 2 on Saturday.

Greinke will be pitching for the first time since he came within two outs of his first career no-hitter Sept. 25 in Seattle in his final regular-season start, so he’s had 11 days of rest.

“Zack is just as good as them,” Rays manager Kevin Cash said. “He just gets there in a different way. He doesn’t have the power, but what he lacks with the power, with the fastball, he certainly can mix pitches with the best of them. Very, very unpredictable. He handles right and lefties very well. He throws the ball down in the zone.”

If the Astros are able to close out the Rays on Monday behind Greinke, Verlander would have seven days of rest before taking the ball in Game 1 of the ALCS on Saturday. The Astros won eight of Greinke’s 10 starts since he was traded, with the veteran going 8-1 with a 3.02 ERA.

“With this rotation, we talked about it all year how they’ve been a stable part of what’s going right here and how we’re winning,” Hinch said. “Historically, and looking at the context of it, I really haven’t paid a lot of attention to it. I just know that their ours and we have a chance to put a good starting pitcher out there every game regardless of venue.”

If the Astros lose Monday, they will turn to either rookie right-hander Jose Urquidy in Game 4 or veteran left-hander Wade Miley. Urquidy posted a 1.50 in September, while Miley’s season came unhinged after a solid five months in the rotation (16.68 ERA in September). At worst, the Astros head back to Houston with Verlander – and Cole ready in relief – but that certainly wouldn’t be ideal.

“Game 3 is what our entire focus is on,” he said.