Tway, who shot a 2-under 70 on Friday, fired eight birdies, including six in a row on the 6,950-yard Vercheres course at Richelieu Valley Golf Club.
With a chance at matching or breaking the course record of 64, the 53-year-old Oklahoman bogeyed the par-4 18th hole to finish 9-under through 36 holes.
The 1986 PGA Championship winner is looking for his first win in 60 events since joining the Champions Tour in 2009.
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.
First-round leader Russ Cochran shot a 1-under 71 to drop into a four-way tie for third with Hale Irwin, Jay Don Blake, and Champions Tour money leader Michael Allen at 7-under. Gary Hallberg and Jerry Pate are one stroke back and tied for sixth.
Rod Spittle of Niagara Falls, Ont., dropped out of a three-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.