Nielsen, who turned 54 on Friday, won 32 titles on smaller tours, including the New York State Open in 1985 and 1989. He entered the final-round at the 7,021-yard Red Course at Eisenhower Park with a three-stroke lead and was never threatened in taking home the $225,000 top prize from a purse of $1.5 million.
He came into the tournament with one top-10 finish this year and was 45th on the money list with $187,921. He has won over $2.2 million since joining the Champions Tour in 2003.
Nielsen's best previous finish as a senior came in a playoff loss to Eduardo Romero in last year's Jeld-Wen Tradition, one of the tour's five majors.
This is the third straight year a player got his first tour win at this tournament. John Harris won last year and Ron Streck won in 2005. Six players have won their first title at this tournament, which started in 1988.
Roberts, who had a one-stroke lead after opening the tournament with a 64, shot a 66 Sunday, closing with a short birdie on the 18th. His second-round 71 proved to be his undoing.
Nielsen shot a 64 on Saturday to take the three-shot lead that tied the tournament record for 36 holes. It was the first time he held the lead alone entering the final round on the Champions Tour.
When he birdied the par-3 5th, he went to 14 under and had a five-stroke lead. He gave a stroke back on the next hole but he kept the comfortable lead with six straight pars before making a two-putt birdie on the par-5 12th that put him four in front of Roberts.
Roberts got within two shots with birdies on 14 and 18 while Nielsen closed with six straight pars.
Nielsen played on the PGA TOUR on a full-time basis from 1978-83 before becoming a club professional near Buffalo. He earned $119,416 in 124 starts on the PGA TOUR from 1979 to 1996, making 75 cuts with two top-10 finishes.
Jay Haas, who won the last two weeks on tour and has four wins this year, closed with a 66, and finished with a 205 total.
Jay Sigel, who entered the final round tied for third, shot a closing 74 and failed in his bid to become the oldest winner in tour history. Sigel, who will turn 64 in November, finished at 208.
The tour heads to Whistling Straits in Wisconsin for the U.S. Senior Open, the first of three majors in a five-week span. Allen Doyle is the defending champion. ... The others to get their first senior win here were Don Bies (1988), Dana Quigley (1997) and Bobby Wadkins (2001). ... Harris closed with a 72 and was seven behind Nielsen. He was trying to become the fifth player to successfully defend the title. ... Mike Fetchick, who won the Hilton Head Seniors Invitational in 1985 on his 63rd birthday, is the oldest tournament champion.