Calcavecchia shot a 6-under 66 at The Old Course at Broken Sound, rebounding from bogeys on Nos. 14 and 15 with the late birdie run. He made a 25-footer on the par-4 17th and set up a 3-foot putt on the par-5 18th with a chip after leaving an approach from the right pine straw to the right of the green.
Langer, the 2010 winner in his home event, had his second straight 66. The 60-year-old German star won seven times last season, and three of the victories were majors.
The 57-year-old Calcavecchia had a 14-under 130 total. He opened with a 64 for a 1-stroke lead in the senior tour's first full-field event of the season.
Calcavecchia won the last of his three senior titles in 2015. He won the 1989 British Open for one of his 13 PGA Tour titles.
Bart Bryant had a 64 to match Jerry Smith (67) at 10 under. Paul Broadhurst (66), Steve Flesch (68) and Michael Allen (68) were 9 under. John Daly followed an opening 67 with a 73 to drop to 4 under. Defending champion Scott McCarron was 2 under after a 69.
Charlie Rymer struggled again in his debut on the 50-and-over tour, shooting a 77. After playing the final six in 4 over Friday in a 75, he was 6 over on the first 11 in the second round.