Anirban Lahiri fired a superb five-under 67 to lie tied third while Shubhankar Sharma carded one-over 73 for a lowly Tied 64th spot after the opening day of the Memorial Tournament here Friday.
While Lahiri had a brilliant back nine, including a hat-trick of birdies, Sharma started his back nine with three bogeys in a row from 10th to 12th and a fourth one on 14th.
Sharma started early in second round, while Lahiri plays late.
Moore opened with five birdies in seven holes and had a great day finding fairways after missing the first one. He posted seven-under 65 for his best start ever at Muirfield Village.
He was one shot ahead of Jordan Spieth, who chipped in for birdie, chipped in for par and holed a 35-foot eagle putt.
Spieth sits one stroke off the 18-hole lead for the second week in a row
Tiger Woods birdied three of his last five holes to shoot two-under 70 and was sitting at T-23.
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Defending champion Bryson DeChambeau carded T78 after an opening-round 74.
Lahiri was tied third with Marc Leishman and Martin Kaymer at 67.
"I feel like my game has been getting better over the last couple of weeks. It's not been a great six or seven months but it's always good coming here. I hit the ball pretty good, I think my yardage control was very good," said Lahiri, who had his best PGA Tour finish here in 2017, when he was Tied-second.
"I hit a lot of balls pin-high, which is really important out here. I played the par-5s better. So, yeah, I'm pretty happy with my round today. Probably could have made a putt or two more. But, yeah, I'll take it.
"It seems all the departments are coming together. It's been a while since I've been able to say that. So it's nice. I feel like my driving has gotten better. I've been working on my iron play, some technique stuff, some equipment stuff. And I think I'm in a good place."
Lahiri got to Muirfield Village on Monday and did some practice and then went back to sleep. He slept through the tornado that hit the place on Monday night.
"Somehow I slept through all of that. I got here on Monday afternoon and got some work in on Monday afternoon, did some range work and just wanted to get really comfortable.
"Like I said I feel like my game has been trending in the right direction. So I wanted to lock that in. I slept through that. I heard about it Tuesday morning. But I was out for the count.
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