Straka chipped in for eagle on the par-5 sixth and played great golf just to keep pace with Scheffler, who had five straight threes on his scorecard to start the third round and was nine under for his round through 15 holes on Saturday (local time).
Scheffler, going for a third straight win at Albany Golf Club in Nassau, has stumbled over the final three holes every round - a double bogey on the 16th on Thursday, a bogey on the 16th on Friday, then a bogey-par-bogey finish.
He still had a 65 and will be in the final group with Straka on Sunday.
Straka seized on the par 5s. Along with his chip-in on the sixth hole, he holed an 18-foot eagle putt on the downwind, par-5 15th.
The Austrian also hit a three-wood that landed perfectly in front of the green at the par-5 ninth that rolled out to 15 feet for a two-putt birdie.
He trailed Scheffler by three shots through five holes, and by two shots with four holes left. But Straka was bogey-free on the day and finished at 18-under 198.Â
"He definitely got it going quick," Straka said of the world's No.1 player. "It didn't look like he was going to miss a putt there for a little bit. But it's golf, it usually evens out a lot and I just tried to focus on my own game."
The only par-4 that Straka birdied was No.7, where the tee was moved back. That kept players from trying to drive the green and instead tested them with a wedge to a dangerous back-left pin. Straka took it on and hit it to seven feet.
Scheffler, who went left of the 16th fairway the opening two rounds - one of those leading to a penalty drop from a bush -this time found the short grass and it wasn't much better. He had an awkward stance, tugged it left into a bunker and the ball buried in the sand, leading to bogey.
He also dropped a shot on the 18th by missing the green to the right - water is left - leaving a tricky pitch up the slope.
"A few unfortunate breaks, but overall did some really good stuff," Scheffler said.
Alex Noren (67) and Hideki Matsuyama (68) were three shots behind Straka, while J.J. Spaun and Wyndham Clark each shot 69 and were four behind.