Stevens twice had the lead down the stretch on the Corales course until a wobbly finish, making bogey on the 16th, answering with a birdie on the par-3 17th and then missing the 18th green for a closing bogey and a 68.
They were at 14-under 202, 1 shot ahead of a large group that included 36-hole leader Matt Wallace of England, Thomas Detry of Belgium and Tyler Duncan, who won his only PGA Tour title at Sea Island in 2019.
“Sixteen, I kind of misjudged the wind and sliced it and made a bogey there. Then 18, I just hit a bad iron shot,” Stevens said. “That was my worst swing of the day. I felt pretty good about everything else.”
All of them had to deal with a relentless wind, which was particularly strong during the closing holes that likely will decide the tournament on Sunday.
Hojgaard, the 22-year-old twin of Rasmus Hojgaard, is a two-time winner on the European tour who is playing on a sponsor exemption.
“In Denmark, it’s quite windy all the time, so I’m used to wind, but it’s still more windy here than it is normally,” he said. “Feeling comfortable. As soon as you hit a couple shots where the ball does exactly what you want it to do and then you just go from there. It’s about using the wind as your friend instead of fighting it all the time.”
Hojgaard missed only one green.
Detry, who had a 65, appears to have an affinity for resort ocean courses. He nearly won in Bermuda last fall, finishing 1 shot behind Seamus Power.
Detry is the highest-ranked player in the field at No. 82, though a victory would not be enough for him to crack the top 50 and get into the Masters. And because Punta Cana is an opposite-field event, winning will not get him to Augusta National.
“I’ve been in this position a couple times and I’m not really thinking about the win,” Detry said. “I’m just going to try and enjoy tomorrow, play like I did today, really. Then you never know what can happen. I don’t really have any expectations, I’m just going to try to enjoy tomorrow and play like I’ve been playing the last three days.”
For Hojgaard, a win would gain him a two-year exemption on the PGA Tour. He is No. 28 in the Race to Dubai points list in Europe. The leading 10 players not already on exemption have access to PGA Tour membership this year.
Wyndham Clark had a 69 and joined the group at 13-under 203. Wallace had a double bogey on his third hole and recovered to salvage a 70, leaving him in good shape going into Sunday.