Diaz carded a nine-under-par 62 to set the early pace at TPC Deere Run in Silvis, Illinois on Thursday.
On the 361-yard par-4 14th hole, Vermeer reached the green in 2 and sunk a 12-foot putt for birdie.
"This has been a weird year for me", said the tour's 164th-ranked player.
Give Diaz some credit though, after struggling to stick on the PGA Tour for several years, he has been playing well lately. The driver has been awesome. (I've been) a little lost but I've been putting in a lot of work on my game, and I felt confident going into today.
The Mexican has a two-stroke advantage over Americans Adam Long and Russell Henley after carding an eagle and seven birdies to get to nine under par.More news: Gold eases after surprise US CPI jump, holds above $1400
Martin Laird of Scotland shot 65 and is tied for fourth with Andrew Landry, Ryan Palmer, Zack Zucher and Ryan Blaum.
The 38-year-old Sharp, winless on the LPGA Tour, had eight birdies and a bogey. The youngest victor on the tour since Jordan Spieth won at Deere Run 6 years ago, Wolff hit 15 greens in regulation and played bogey-free. She was born in nearby Toledo and has an endorsement deal with Marathon Oil.
There is a surprising name atop the leaderboard after one round at the John Deere Classic.
Play was suspended at 12:55 p.m. local time, and called for the day at 5:05 p.m. after just over an inch of rain soaked the course.
Long, who claimed his first PGA Tour victory earlier this year in the Desert Classic, and Henley, a three-time victor on the PGA Tour, each carded four birdies on both nines in their 64s.More news: Federer, Nadal braced for Wimbledon epic
"Conditions were pretty easy when we started the round".
He said there was a lot less stress thanks to the two-year exemption he received, but the game was the same challenge. "Wind picked up there the last two hours". I played good at Travelers.
He was joined atop the leader board by Romain Wattel, Nino Bertasio and Edoardo Molinari.
The best finisher on Sunday not already exempt for the British Open will earn the final seat on the overnight charter flight to Royal Portrush for next week's major championship in Northern Ireland.
Lee Slattery, Erik Van Rooyen, Thomas Pieters, Andy Sullivan, Jamie Donaldson, Kalle Samooja and Thomas Aiken had 64s.More news: The Management Of Moon Program Was Shaken Up By NASA