Tanigawa rebounded from bogeys on Nos. 8 and 9 with birdies on Nos. 10-12, 14, 15 and 17 at The Classics at Lely Resort.
"I never felt all that comfortable early on and it kind of showed," Tanigawa said. "I kind of hung in there, then I made those two bogeys on 8 and 9, which was easy to do. I made a nice putt on 10 to make a birdie and just tried to stay patient and plug away. I started hitting better shots and making some putts and got some momentum my way."
He won the PURE Insurance Championship in September at Pebble Beach for his lone PGA Tour Champions title.
Day birdied the final two holes for a 66.
"I made a double on the front nine," Day said. "Other than that, everything was real solid. You're going to get a lot of birdie opportunities out here, so you've got to stay patient."
Ames, tied for the first-round lead with Sandy Lyle after a then-course record 63, had a 68 to keep a share of the top spot at 11-under 131.
"I'm quite happy to be in the position I'm in," Ames said. "Tomorrow's another day."
Kevin Sutherland broke the day-old course record with a 62, birdieing six of his first eight holes in a round that started on No. 10.
"I hit it better than I did yesterday and got in a rhythm early and I putted well," Sutherland said. "I made all the putts I needed to make and made a couple that probably were a gift."
Sutherland was a stroke back with Bernhard Langer (64), Colin Montgomerie (63), Woody Austin (65), Tom Byrum (65), Dan Olsen (67) and Kent Jones (67).
The 61-year-old Langer, the Oasis Championship winner last week near his home in Boca Raton, won the event in 2011, 2013 and 2016.
Tour newcomer Retief Goosen (65) and Steve Stricker (66) topped the group at 9 under.
"I've been giving myself some opportunities around here the first couple of days and just not getting it in there, not knocking 'em in," Stricker said. "I'll hit good putts, a lot of misreads. I'll hit a few bad putts. I'm just struggling on getting it in the hole."
Lyle followed his opening 63 with a 71 to drop into a tie for 15th at 8 under. Jay Haas also was 8 under, shooting a 70 a day after the 65-year-old player bettered his age with a 64.
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