NEWTOWN SQUARE, Pa. — By all accounts, Justin Rose shouldn’t even have been playing in Saturday’s third round of the PGA Championship at Aronimink.

It took a holed-out chip-in for eagle on his final hole of the second round Friday on the par-5 ninth, to get Rose, who was 5 over at the time, inside the 4-over-par cut line.

He took full advantage of the opportunity to play Saturday’s third round, shooting a 5-under-par 65 to equal the low round of the tournament, and walked off the course 2 under par, and by the end of the day, he still was just four shots off the lead held by Alex Smalley.

“A bit of freedom,’’ Rose said of his feeling after making the cut the way he did. “Obviously, a bit of gratitude just to be here. It offered me the opportunity to go and try and find something within myself and within my game [Saturday]. I relished that opportunity.’’

Rose came out on fire Saturday, carding four consecutive birdies on Nos. 3, 4, 5 and 6 and shot 30 on the front nine.

“I got off to a good start, which is kind of exactly what I felt like I needed to do today,’’ Rose said. “It was some beautiful conditions this morning. I put the ball in play off the tee, which I wasn’t able to do for the first two days, and hit some really beautiful iron shots into some pins.’’

The 45-year-old Rose’s 30 on the front was the fourth time in his major championship career that the Englishman shot a nine-hole score that low.

He’s just the fourth player 45 or older since 2000 to shoot 30 or lower on either the front or final nine holes of one major championship round.

“I was really happy with the way I kind of adjusted overnight and worked on a couple of things on the range before I went out to play [Saturday], just adjusted a couple of things,’’ he said. “It was good to see that pay off so quickly.’’

Rose, who recently switched to irons made by McLaren Golf, a brand new to the business, a move questioned by many as the brand’s first global ambassador.

“I played so poorly the last few weeks that it is what it is,’’ Rose said, making no equipment excuses. “If you put a poor move on it, I don’t care what you’re playing. I’m very confident. I’m very experienced. I’m very curious. I’m very detail oriented. I won’t be doing anything stupid.

“I know these [irons] are great. I’ve worked really hard on the process. It was good to kind of play well [Saturday] and see the evidence of that statistically.’’

Rose said as he walked down the seventh fairway, he joked with his caddie, Mark “Fooch” Fulcher: “We were suddenly 1 under par for the tournament, and we were 5 over par like seven holes ago.’’

“I said, ‘You wouldn’t have thought I’d be walking down No. 7 under par in the tournament, would you?’ ’’ he said.

Now, he’s 2 under with a chance to win the second major championship of his career — and second in the Philadelphia area, having won the 2013 U.S. Open at nearby Merion.

“Obviously, Merion will be a place close to my heart forever,’’ Rose said. “I try to come back to Merion once every year. It’s one of my favorite places to play.’’