Bohn held the lead after sinking a 25-foot putt for an eagle at the 13th, but a closing bogey saw him relinquish his advantage.
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The 29-year-old, whose only career triumph to date remains the 2014 Web.com Tour Championship, sank four birdies on the front nine and one on the way back to turn in a bogey-free card.
The American did not drop a shot during his third round as he bids to become the sixth consecutive first time victor in six events on the PGA Tour so far this season.
“As I went down to get them, I figured I could be going home very soon”, McDowell said.
Russell Knox, coming off his first win last week in Shanghai at the HSBC Champions, also made bogey on the last hole for a 65. “The only thing I can draw on is how I’ve been playing”.
McDowell and Knox were tied for the lead on 19 under when darkness suspended play shortly after 6pm local time following an earlier three-and-a-half-hour delay at the El Camaleon Golf Club.
The four leaders finished one shot ahead of a group that included Michael Thompson, D.J. McDowell has already played the par-5 13, one of the easiest holes on the course, and faces a stern test on the par-4 14. PGA Tour rookie Harold Varner III birdied four of his last five holes for a 62 to join Si Woo Kim (64) two shots behind.
To capture his second trophy in as many weeks, though, Knox will have to pull clear of McDowell, who is looking for his first piece of hardware in almost three years. A 12-foot birdie on the 17th allowed him to salvage a 70.
Justin Leonard had a rapid onset of what he expects to be his shortest season opening a 6-under 65 on Thursday in the OHL Classic in Mayakoba only to share the lead with Aaron Baddeley, Derek Fathauer and Shawn Stefani, who was a finalist at the OHL Mayakoba previous year.
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McDowell has five holes to play, while Knox must complete six holes.
