Straka needed to birdie the 18th at TPC Deere Run on Sunday to card a stunning closing 59, but pulled his approach into the water left of the green.
The resulting six meant Straka had to settle for a nine-under 62 and setting the clubhouse target at 21 under par, with six groups still to finish.
A birdie on the 14th took Brendon Todd to within a shot of the lead, only for the American to then three-putt the 16th and fail to birdie the par-five 17th.
Todd finished in a tie for second on 19 under with playing partner Alex Smalley, with Sweden's Ludvig Aberg another stroke back in a tie for fourth with Adam Schenk.
Aaron Baddeley shot a six-under 65 to finish in a tie for 31st at 11 under. Fellow Australians Geoff Ogilvy (68) and Harrison Endycott (73) completed their weekends at nine and four under, respectively.
Straka, who had recorded an eagle and nine birdies in his first 14 holes, said: "The 59 was nowhere in my head really.
"I knew I had a chance but in that situation the only thing that matters is trying to win the golf tournament.
"It was not a good shot (on 18). I was really just trying to go middle of the green, pulled it early and the wind dragged it over to the water. It was unfortunate but the first bad shot I hit all day so I'll give myself a bit of slack."
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