The 53-year-old Tway had a 9-under 135 total on Vallee du Richelieu Golf Club's Vercheres Course.
The Oklahoman had eight birdies, including six in a row on Nos. 7-12. With a chance at matching or breaking the course record of 64, he bogeyed the par-4 18th.
''It was disappointing to finish that way, but it was still a nice round,'' Tway said.
Winless on the 50-and-over tour, he won the 2003 Canadian Open for the last of his eight PGA Tour titles.
''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,'' said Tway, the 1986 PGA Championship winner. ''You keep plugging along and practicing.
''I'm seeing signs of much better play, but my scoring has been poor for a long time. 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 67. The 1989 British Open champion claimed two of his 11 PGA Tour wins in Canada, the 1997 Greater Vancouver Open and 2005 Canadian Open.
''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.''
First-round leader Russ Cochran had a 71 to drop into a tie for third at 7 under with Michael Allen, Hale Irwin and Jay Don Blake. Allen, the tour leader with two victories and earnings of $1,071,282, had a 69, Irwin shot 68, and Blake had a 67.
The 67-year-old Irwin, the Champions Tour career leader with 45 victories, is trying to become the oldest winner in tour history. Mike Fetchick was 63 years to the day when he won the 1985 Hilton Head Seniors Invitational.
''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.''