Morgan and Roberts both posted rounds of 3-under 69 to get in the clubhouse at 6-under-par 138. Nielsen's heroics on 18 got him into the tie at Sonoma Golf Club.
Jay Haas, who has won his last two starts on the Champions Tour, carded a 3-under 69 and is tied for fourth place with Craig Stadler (70), Des Smyth (70), Tom Watson (70), Bruce Fleisher (71) and Jerry Pate (72). The group is one shot back at minus-5.
This title is not the only thing at stake this week. The $1 million annuity and the year-long Charles Schwab Cup title are on the line with Dana Quigley leading Hale Irwin by 345 points.
There are several players in the mix for the Cup, but Quigley has the advantage. He was alone in the lead at 7 under par, but fell apart with a bogey at 15 and a double bogey at the 16th.
Quigley shot a 1-under 71 and is tied for 10th with Tom Kite (68) and Morris Hatalsky (70) at 4-under-par 140. Irwin managed a 2-under 70 and is tied for 16th at minus-2.
Nielsen struggled early in Friday's second round. He bogeyed the third, fourth and fifth holes to fall down the leaderboard, but rebounded around the turn with a birdie at the ninth.
He birdied 11 to get to 1 over on the round, but dropped another shot at 15, only to make that bogey with a birdie one hole later.
At the closing hole at Sonoma, Nielsen hit a poor second shot well left of the flag. Nielsen, winless on the Champions Tour, holed the long birdie try to join the lead.
Morgan, the 1997 Charles Schwab Cup Championship winner, recorded birdies at four and five, then rolled in a 4-footer for birdie at the ninth. Morgan dropped a shot at the 14th, but took advantage of the last par-5, the 16th.
At that hole, Morgan sank a 6-foot birdie putt to reach 6 under par for the championship. His birdie putt from 21 feet came up one revolution short at 17, then the 23-time winner on the Champions Tour played solid golf on 18.
His approach landed in a greenside bunker, but he blasted out 12 feet short. Morgan calmly rolled in the par save to claim his piece of the lead.
'It's a nice feeling,' said Morgan, who needs a win this week to extend his streak to 10 consecutive years with a win on the Champions Tour. 'Obviously I'd like to keep the streak going, but if ends this week, so be it.'
Roberts, who collected his only Champions Tour win at The Tradition, made the turn at 1 under par thanks to a 4-foot birdie putt at the par-4 ninth hole.
He birdied the 10th. bogeyed 11 and 12, but birdied 13th to stay 1 under on his round. Roberts birdied the 16th to get to 5 under for the championship, then drained a 10-foot birdie putt at the 17th to join the lead at minus-6.
On the 18th, Roberts hit a 6-iron just off the green on the right side. He was able to get up and down for par and now has a good chance at his second win on the elder circuit in his rookie year.
'It's wide open with 15 people within three shots,' said Roberts. 'It's hard to separate yourself. We'll see what happens tomorrow and Sunday. I think it's going to be a shootout all week.'
Jim Thorpe (68), Brad Bryant (70) and Tom Purtzer (71) are the other players within three as they are knotted at minus-3.
Defending champion Mark McNulty posted his second consecutive round of even- par 72 and is tied for 21st place at 144.