Morgan closed with a four-under 67 to end at 16-under-par 197 for his 24th victory on the Champions Tour -- placing him in a tie for third place all-time with Miller Barber.
Roberts was on the brink of wrapping up his fourth victory this season -- his first full campaign on the Champions Tour -- before his gaffe at 17. Instead, he also finished with a four-under 67 to end a shot back at 15-under-par 198.
Hajime Meshiai shot a three-under 68 on Sunday and ended in third place at 13- under-par 200. Keith Fergus also shot a 68 to finish fourth at minus-11, while Allen Doyle fired a 67 to end one shot further back in fifth.
Morgan now trails only Hale Irwin (44) and Lee Trevino (29) in career Champions Tour victories.
This one came with a little help from his Sunday playing partner.
A one-shot overnight leader at minus-12, Morgan was overtaken by Roberts after he bogeyed the par-four sixth to fall to 11-under.
Morgan birdied the ninth to get that shot back, but it didn't matter. Roberts posted a flurry of birdies on the front nine -- at the fourth, seventh and eighth -- to get to 14-under around the turn for a two-shot advantage.
Another bogey for Morgan at the 10th dropped him three shots behind, but he made up one stroke by posting four birdies over the next five holes while Roberts collected three over the same stretch.
Then, at the penultimate hole, Roberts pulled his approach shot into the water.
It wouldn't have been so bad, but Morgan ended up rolling in a 35-foot birdie putt and Roberts missed a six-footer for bogey. With a chance for birdie at the 18th, Roberts missed a nine-foot putt with a chance to tie.
'This might be one of the few (victories) I've thrown away in my career,' said Roberts. 'I'm playing well, however. I just made a couple of bad swings.'
Morgan's win netted him $225,000 one week after he squandered a third-round lead at the Senior PGA Championship. That's a $93,000 difference from Roberts' second-place check.
'Last week was a little bit of a disappointment, but it was nice to come back from that,' said Morgan. 'I felt bad for Loren because he played well for most of the day.'
James Blair, Ed Dougherty, Morris Hatalsky and Kirk Hanefeld shared sixth place at nine-under-par 204. Danny Edwards, Bruce Lietzke, Fuzzy Zoeller, David Edwards, Tom Purtzer and John Harris finished one shot further back in 10th.