Langer, who threw away a two-stroke lead on the final hole at Royal Birkdale last year and then was beaten for the title in a playoff, was out in a best-of-the-day 31.
He birdied the third, fourth, sixth and eighth holes, and went 5 under when he birdied the long 13th. He dropped a shot at the 16th but then hit back immediately with birdies at the two closing holes.
Langer is trying to add a second British Senior title to the one he won at Carnoustie in 2010.
Tway, a former golfer at east Cobb’s Wheeler High School, set the early target at 4-under 67, with birdies at the first, sixth, 12th and 13th, and no dropped shots.
Chris Williams of England was alone in third on a bogey-free 68 with birdies at Nos. 2, 4 and 6, while Andrew Oldcorn of Scotland was a stroke behind in fourth. Spain’s Pedro Linhart and Canadian Rick Gibson were tied for fifth on 70.
Mark Wiebe, who beat Langer in last year’s playoff and played with him in the first round, carded 5-over 76.
Colin Montgomerie, bidding for his third successive seniors’ major, was on 74 with just two birdies, and three dropped shots.
Tom Watson had a roller-coaster front nine of 1-over 36, steadied the ship for five holes after the turn, then dropped three strokes on successive holes before birdieing the last for a 3-over 74.
The winner at Royal Birkdale two years ago, Fred Couples, was out in 39 after a triple-bogey eight at the long sixth, but stormed back with a birdie-eagle-birdie run from the 12th to get back to level, dropped a stroke at the 16th, and birdied the last to be back in 32 for a par 71.
Canadian Open: Tim Petrovic and Michael Putnam shared the first-round lead, shooting 6-under 64 in sunny, breezy afternoon conditions at rain-softened Royal Montreal.
The 47-year-old Petrovic was the last player to get in the field, grabbing a spot when Benjamin Alvarado withdrew Tuesday.
Petrovic eagled the par-5 12th hole and had four birdies in his bogey-free round. He won his lone PGA Tour title in New Orleans in 2005.
The 31-year-old Putnam had six birdies in a bogey-free round, hitting 11 of 14 fairways and 14 of 18 greens in regulation.
Winless on the PGA Tour, Putnam won twice on the Web.com Tour last year and topped the regular-season money list.
Canadian amateur Taylor Pendrith and Kyle Stanley were a stroke back, and former Masters champion Charl Schwartzel, Nick Watney and Robert Allenby topped the group at 66.
The 23-year-old Pendrith, making his first PGA Tour start, is coming off his senior season at Kent State.
Two-time champion Jim Furyk and Canadian David Hearn shot 67, and Brandt Snedeker, the winner last year at Glen Abbey in Oakville, Ontario, had a 69.
Canadian Mike Weir, an eight-time PGA Tour winner making his 24th start in the event, had a 70.
International Crown: Yani Tseng made a 12-foot birdie putt on the 18th hole to give Taiwan a sweep of the top-seeded United States team in the opening round of the women’s team match play event.
Tseng and Phoebe Yao never trailed in a 1-up win over Stacy Lewis and Lexi Thompson. Earlier, Candie Kung and Teresa Lu beat Paula Creamer and Cristie Kerr 4 and 3.
The inaugural International Crown features 32 players from eight countries.
Each team receives two points for a win and one for a tie. The U.S. was the only team that failed to secure a point on the first day.
Today, the United States (0 points) will face Spain (3) in Pool A, and Taiwan (4) will take on Thailand (1). Pool B matchups are Japan (3) against South Korea (2), and Australia (2) versus Sweden (1).