Jim Thorpe posted a 5-under-par 67 to finish alone in fifth place.
Morgan got off to a quick start at the TPC at River's Bend with a birdie at the opening hole and added a birdie at the ninth to make the turn at 2 under.
Despite the solid start, Morgan really turned it on down the stretch and torched the back nine to surge to the top of the leaderboard.
Morgan hit a pitching-wedge to four feet at the par-5 11th and converted for a birdie. He then dropped a 9-iron inside six feet for a birdie at the par-4 13th and ran home a putt of the same distance for a birdie at the 15th.
At the par-4 17th, Morgan continued his stellar iron play and hit his approach within five feet of the hole for a birdie. He followed that up with a birdie at the par-5 18th to hold the outright lead after the opening round.
'I missed some opportunities on the front but on the back I got it pretty close,' said Morgan, who won this event in 1999. 'I didn't make many long putts today. I fired at the pins a lot today.'
Nelson parred his first five holes before catching fire late on the outward half. He picked up a birdie at the sixth and made it two in a row at the par-3 seventh after his tee shot stopped 10 feet from the cup.
At the par-5 eighth, Nelson knocked a 4-wood to 15 feet and ran home the putt for an eagle. Nelson then dropped a 5-iron within five feet at the ninth for another birdie to reach 5 under around the turn.
Nelson added a birdie at the 11th but he found trouble with a bogey at the par-4 14th. Nelson regained a share of second at the par-4 17th after his 7-iron approach left him with a 10-foot putt for birdie and a round of 66.
'Decided today I was going to just stroke my putts, not hit them,' said Nelson, who missed time over the summer due to a hip injury. 'I had to change my swing a bit which helped.'
McGee had six birdies and no bogeys for a 66 of his own.
'It's nice to play well in your home state,' said the Ohio native. 'No bogeys, which is always fun.'
Doug Tewell collected five birdies and a bogey for a round of 68. Tewell was joined by Seiji Ebihara, Gary Koch, Tom Wargo, Graham Marsh, Tom Jenkins and J.C. Snead at 4 under par.
Defending champion Bob Gilder was one stroke back in a large group tied for 13th. Gilder finished alongside Don Pooley, Wayne Levi and Jay Sigel among others at 3-under-par 69.