"The Augusta University product squared a lone bogey-5 (3-putt from 38'1"), camouflaged by six birdies at holes 4, 8, 10, 12, 17 and 18, four from between eight and 12 feet.
Noren, a four-time victor on the European Tour previous year who is No. 12 in the world, missed a 5-foot birdie putt on the final hole that would have tied him for the lead.
In a scramble for the top - 18 players were separated by four shots after 54 holes - Reed finished strong.
Italian halfway leader Francesco Molinari (72) is in a group of four players two shots behind Reed, while world number one Dustin Johnson is equal 14th, four shots back after matching Reed's 67.
When it got underway, players encountered challenging winds, in which Power posted a one-under par 71 and Hurley carded a three-under 69 for a five-under par total of 139. Rahm hopes to grab his second victory of the year and continue his phenomenal first full season on the PGA Tour.
Also tied for fifth are Vaughn Taylor (69), Brian Harman (69), Grayson Murray (73), Smylie Kaufman and Ben Martin, the latter two yet to complete their rounds.
Chris Sale won't be suspended for throwing behind Manny Machado
Manny Machado and the Orioles finally are out of Fenway Park, following the most eventful - and ugly - series of the season. Red Sox: Knuckleballer Steven Wright will have surgery to fix cartilage in his left knee and miss the rest of the season.
Said Rahm: "I kept waiting for something good to happen on the back nine, but that chip-in was just a bonus". It was the first time he has had the lead after the opening round on the PGA Tour. He said he was getting used to courses he had not played much before and feels things are coming together this season.
"I didn't get ahead of myself today", said the 26-year-old, who played conservatively for the middle of the greens.
Ariya Jutanugarn won a sister showdown Friday in the Lorena Ochoa Match Play, and Lydia Ko, Michelle Wie and Cristie Kerr also advanced at Club de Golf Mexico.
He is joined by major winners Graeme McDowell of Northern Ireland and fellow American Phil Mickelson on that mark. While better than a disqualification, a four shot penalty is still pretty painful (especially in the midst of a 4-over round), and practically just as hard to recover from.
Wie will face the third-ranked Jutanugarn, a 19-hole victor over Cristie Kerr in the event that switched from stroke to match play and moved from November. He closed out his round by pulling a drive on the par-4 ninth hole, punching under tree limbs to short of the green and again pitching it short.
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