Watney is at 12-under 204 after 54 holes.
Ken Duke, who had a 6-under 66 in the third round, moved into second place at 206.
Second-round leader Mark Calcavecchia shot even-par 72 Saturday. He is tied for third at 207 with Scott Gutschewski (67).
First-round leader Kyle Reifers is fifth at 208.
Watney turns 26 Tuesday.
"I'm excited for Sunday," said Watney, who won once on the Nationwide Tour, but is looking for his first PGA Tour crown.
Fifteen players, including four of the last five champions, have made this their inaugural win on tour.
"I feel comfortable, but I don't want to get too far ahead of myself," said Watney. "I've still got a long way to go."
Swim Week Miami Beach 2014 [PHOTOS]