Fuzzy Zoeller, the defending champion, shot a third-round 70 and shares fourth place with second-round co-leaders Allen Doyle and Gil Morgan. The trio is at 1-under-par 209.
The third round was completed Sunday morning after heavy rainfall suspended play on Saturday. The final round is scheduled to tee off shortly after the third round with players remaining in their groups from the third round.
Smyth, a former member of the European Tour, finished eight holes on Saturday before play was stopped. He parred No. 9 on Sunday but rattled off a 20-foot birdie at the 10th and a 25-footer at the 12th.
While most of the competition was dropping down the leaderboard, Smyth kept moving up. He tallied a birdie at the 15th when he knocked a 4-iron to 12 feet and closed the round with a tap-in birdie at the par-3 17th to take sole possession of the lead.
'I felt relaxed today and I didn't feel relaxed the first two days and I struggled a bit,' said Smyth. 'I was happy to be 1-over par after two rounds. I thought the course was difficult.'
Dick Mast and Doug Tewell share seventh place at 1-over-par 211.
Seiji Ebihara held the lead when play was called Saturday. He stood at 4-under par for the championship and was 2-under through five holes when the horn sounded but Ebihara struggled badly on Sunday morning.
Ebihara collected three bogeys and two double-bogeys for a round of 5-over 75. He is tied for 16th place at 3-over-par 213.