The 2003 Canadian Open champion hopes a Montreal Championship title will end that drought.
Tway shot a 7-under-par 65 on Saturday to take a one-stroke lead over Mark Calcavecchia on the second day of the 54-hole US$1.8 million tournament.
Tway, who shot a 2-under 70 on Friday, fired eight birdies Saturday, including six in a row on the 6,950-yard Vercheres course at Richelieu Valley Golf Club in the only Canadian event on the PGA's Champions Tour.
With a chance at matching or breaking the course record of 64, the 53-year-old from Oklahoma bogeyed the par-4 18th hole to finish 9-under through 36 holes.
"It was disappointing to finish that way but it was still a nice round," Tway said.
The 1986 PGA Championship winner is looking for his first win in 60 events since joining the Champions Tour in 2009.
"I haven't played like I think I'm capable of playing since I've been out here but that's just the nature of the game," Tway said. "You keep plugging along and practising."
Tway is playing his 207th tournament overall since his last victory in a playoff over Brad Faxon at Hamilton Golf and Country Club in Ancaster, Ont.
"I'm seeing signs of much better play but my scoring has been poor for a long time," Tway said. "If you don't chip the ball well, if you don't wedge the ball well and if you don't putt the ball well, it's tough to score. This week has been a little bit better, and therefore I'm doing better."
Calcavecchia shot a 5-under 67 and moved up to sole possession of second place from an 11-player logjam for sixth after opening with a 3-under 69 on Friday.
The 1989 British Open champion referenced his previous success in Canada. Calcavecchia claimed two of his 11 PGA Tour wins in Vancouver, including the 1997 Greater Vancouver Open and the 2005 Canadian Open.
"You know, I had some chances at Glen Abbey, but obviously I play well north of the border for some reason," Calcavecchia said. "It's a long way to go. We'll see what happens (Sunday). We'll talk about it if I happen to get the job done."
Calcavecchia set a PGA Tour record when he reeled off nine consecutive birdies at the 2009 Canadian Open.
Tway and Calcavecchia will play Sunday's final round with Jay Don Blake, who shot a 5-under 67 to finish in a four-way tie for third at 7-under.
Hall of Famer Hale Irwin and Champions Tour money leader Michael Allen will tee off Sunday with 18-hole leader Russ Cochran, who dropped back to third after shooting a 1-under 71.
The 67-year-old Irwin followed up an opening-round 69 with a 68 on Saturday.
"I birdied the 16th hole to go 4 under par and I figured if I can birdie one of the last two and shoot my age, I'll be really happy with that," Irwin said. "I hit two really good irons to both greens and they landed, hit very, very hard, and bounded well past the hole, and fortunately I two-putted both of those from 35 or thereabouts.
"I came close on both putts but it's disappointing in that I had opportunities. I put the ball in the fairway and I had a chance to have a better chance at shooting my age again than not."
Gary Hallberg and Jerry Pate are one stroke back and tied for sixth.
Rod Spittle of Niagara Falls, Ont., dropped out of a four-way tie for second after shooting a 72 on Saturday to stay at 4 under.
He is tied for 12th and remains the top Canadian among the six entered in the field of 81 senior golfers in the third edition of the PGA Champions Tour event, which was held at Fontainebleau Golf Club in Blainville, Que., prior to this year.
Spittle shot a tournament-record 62 on the final day of last year's tournament.
Jim Rutledge of Victoria, B.C., shot a 4-under 68 to reach par after a disappointing 4-over 76 on Friday.
Marc Girouard of St. Sauveur, Que., the only Canadian other than Spittle to break par Friday, is 3 over after following up a 71 with a 76 on Saturday.
Yvan Beauchemin of Louiseville, Que., is 4 over after a 1 under 71 second round.
Blainville's Claude Tremblay, who recorded the three-year-old tournament's first hole-in-one on Friday, is 8 over, and Jean Laforce of St. Gabriel de Brandon, Que., is 10 over.