Brooks Koepka tees off on the second hole during the third round of the Zurich Classic at TPC Louisiana in Avondale on Saturday, April 26, 2014. (AP Photo/Jonathan Bachman)

After getting into the Zurich Classic of New Orleans through a Monday qualifier and making the cut to stick around for the weekend, Brooks Koepka must have figured he was playing with house money Saturday.

Koepka was standing in the fairway at the par-5 18th hole at TPC Louisiana when he took a rip at the flag stick, which was tucked precariously close to the lake that runs the length of the hole.

Already 5-under-par for the day and 10-under for the tournament, Koepka took a chance to make a move up the leader board going into Sunday’s final round — only to come up empty.

Minutes later, after taking a drop and chipping onto the green, he calmly rolled in a 4-foot, par-saving putt to cap a round of 67.

“I told my caddie that I feel very relaxed this week,” Koepka said. “It’s not that I’ve been uptight or tense or anything like that in previous weeks, but it’s almost like I don’t care this week. I hit in the water on 18 and didn’t even flinch. It was one of those things. … It wasn’t my best shot, but I played good.”

That’s what a few weeks of rest and relaxation will do for a world traveler like Koepka, who plays mostly on the European and Challenge tours.

Rested and ready to go after taking a couple of weeks off, Koepka earned his spot in the 156-man field Monday along with three other golfers when he carded a 64 at LaTour Golf Club in Mathews.

Ironically, Fore!Kids Foundation officials wanted to give Koepka, the world’s 75th-ranked player, a sponsors’ exemption to their tournament. But the Florida State graduate had already played in seven events on sponsors’ exemptions — the maximum allowed in a season — which meant he had to get in the old-fashioned way.

He did and shot a 71 on Thursday and a 68 on Friday to make the cut, the only one of the four who earned spots in the tournament to get to the weekend. He’s tied for 16th going into the final round.

Koepka, who has won $387,247 in eight PGA Tour events this season, will try to add a considerable amount from the $6.8 million purse Sunday.

Since he has no status on the PGA Tour and has used up all of his exemptions, he has to make hay when he can — which is what he was thinking when he took aim at the pin Saturday.

“Basically, good play takes care of itself,” Koepka said. “If you play good, everything will be fine. So that’s the way I’m looking at it.”

Even though he’s eight strokes off the lead with a round to go, Koepka isn’t giving up on his dream of winning a tournament — which would be most unlikely, considering he came out of the open qualifier. Still, he’s not surprised by his solid play.

“Actually, I hadn’t played that much golf,” said Koepka, who played in the 2012 U.S. Open and British Open and PGA Championship last summer. “I went and visited my girlfriend (a pro soccer player in Sweden) and didn’t touch a club for two weeks. I don’t want to say this (week) is a surprise, but I needed a little break. Don’t get me wrong — I love golf. But I had a little bit too much of it for six or seven straight weeks. I needed the time off to recharge the batteries — mentally, physically, everything.”

So getting into the Zurich Classic, one way or another, was the goal.

“I was over here, and I wasn’t planning on going over to Asia,” he said. “So I figured, ‘Why not?’ There was no point in sitting around at home. I’d rather be out here with these guys.”

A top-10 finish Sunday would earn him a spot in the Wells Fargo Championship next week. But he’s not selling himself short.

Koepka said he went into the weekend needing to shoot 12-under in the final two rounds to have a shot at winning. That became a little more realistic when second-round leader Ben Martin backed up to the rest of the field with a 73 on Saturday.

“I felt like I’d have a chance with 12-under on the weekend,” he said. “I gave myself a chance to do it — go shoot 7-under (Sunday). You never know what can happen, so I just have to stay patient.

“It feels nice to be comfortable and just be very relaxed, because that’s my personality. I don’t get uptight about anything.”

Not even an errant shot.