At 13-under-par, Morgan is one stroke lower than Jim Ahern, and two shots clear of Tom Wargo and Bruce Fleisher.
Morgan began and ended his day with a birdie. In between, he added five more red numbers and two bogeys for a round of 5-under-par 67.
Ahern carded the round of the day, a bogey-free 8-under-par 64. Ahern, who won the 1999 AT&T Canada Senior Open Championship posted eight birdies through his first 14 holes on Saturday.
Fleisher made an early move in the third round by birdying the 2nd, 3rd and 4th holes, but the Tour's leading money earner could only muster two more birdies to one bogey over his final 14 holes.
Morgan is in search of his third victory of the 2000 campaign. Morgan won his first start of the year at the Emerald Coast Classic, and then captured The Instinet Classic in July.