Poston went wire-to-wire at TPC Deere Run to earn his second PGA Tour victory and a first trip to The Open after seven previous major appearances.
Three shots clear overnight, the 29-year-old showed no sign of nerves as he strengthened his position with birdies at the first, second and third holes.
Bogeys followed at the fifth and sixth, but Poston nevertheless maintained his position at the top of the leaderboard and another gain at the 17th enabled him to finish with a two-under 69 for a three-shot victory on 21-under-par.
"It was a great week," Poston said. "My game is in a great spot and to get it done wire to wire is special. And to punch my ticket to St Andrews… it is a Championship I have never played in and one that I always wanted to play. For my first one to be in St Andrews is pretty special.
“I remember watching the guys coming up 18 in St Andrews. Just seeing the people and the way the fans are over there. They are very knowledgeable about golf, and it is really cool. I can’t imagine a better feeling than walking up 18 at St Andrews.
“I don’t have any experience with links golf, so I will have to definitively learn as I go when I get there. But I am excited. It is the home of golf, it is the way the sport was originally played, so I am excited to experience it and hopefully do well.”
Bezuidenhout, who has played in each of the last two Opens, secured a third successive start in golf’s original Championship thanks to a fine finish on Sunday.
Birdies at 14, 15 and 17 helped the South African to a bogey-free 66 and a share of second with Grillo, who was round in 69 to also finish on 18 under.
Bezuidenhout said: “The whole week was a progression. I started it slow, and I knew there were birdies to be made on this golf course. I started with a two under score on Thursday and knew I needed good things to happen. And it did, I just kept my patience and played to my strengths. I am just really, really pleased with the result at the end of the week.
“To play in The 150th Open at the home of golf is going to be really special. The fans are massive. They respect the game of golf, they respect the players, they respect good golf and good shots. I love the whole vibe about it. It is the oldest Open in the world and such a prestigious golf championship. To qualify for The Open at one of my favourite courses in the world is very special. It is always a special week there with so many historic moments on that golf course.
“Growing up, Ernie [Els] was always my idol. Luckily, I am pretty good friends with him and we will probably play a few practice rounds together at St Andrews.”
Bezuidenhout and Grillo finished one shot clear of Christopher Gotterup, Callum Tarren and Scott Stallings. The latter could have stolen the final qualifying berth from Grillo courtesy of a superior world ranking had Stallings birdied the last.
Grillo has made the cut in two of his previous five Open appearances, finishing tied-12th on each occasion in 2016 and 2021.
“Today was one of those moments when you feel on top of the world," Grillo added.
“If it is windy [at St Andrews] it is going to be tough and if it is not windy it will be a very accessible golf course. St Andrews is one of my top three places to play golf in the world and I am looking forward to it, especially because it will be in The Open.
“I remember hitting the ball on 18 once. The first time I was there for the Dunhill Links, the weather was perfect and there was no wind at all. I got to experience the golf course with calm conditions and then a couple of days later it was super windy and cold. It was almost impossible to play out there. It is a golf course where you can go very low or shoot high seventies very easily.
“It is a special event with all the history. It is a big deal for Argentinian golfers. De Vicenzo won one and I am looking forward to having another chance to give my best in The Open and hopefully I can bring another one home.”
The John Deere Classic was the latest event in The Open Qualifying Series, which offers golfers around the world opportunities to reach the landmark Championship at St Andrews from 10-17 July.
Four spots in the field are available in the final week before The Open, with the Genesis Scottish Open offering three places and the Barbasol Championship providing the last route into the Championship.