Four Illini were among the top 10 individuals, led by senior Nick Hardy who tied for fourth at 2-under par.
Junior Bennett Baker capped another good year by tying for 33rd at 3-over, shooting a 1-over 73 in the final round.
Furr led all individuals in the field with 16 total birdies on his way to finishing tied for third overall with a 9-under par 207.
But the Jayhawks, Cardinal and three other teams are all headed to the 2018 NCAA Division I Men's Golf Championships.
The Spartans shot a 7-over-par 291 in the final round at the OSU Scarlet Course and finished in seventh place at 32-over-par 884 (303-290-291), just two spots out of the qualifying for the NCAA Championships. Baylor's only better Regional scores were at the 2017 Stanford Regional, recorded by Dossey (201), Matthew Perrine (207) and Hunter Shattuck (207).
Tomlinson, the first Ute to play in the NCAA Regionals since 2007, shot a 1-under 71 on the final day of the three-day tourney. States Fort posted an even-par round of 72 and Thadd Obecny II was 1-over par. Andy Stewart tied for third in 2001.More news: Senate votes to protect net neutrality rules
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After hitting a 330-yard drive to setup his eagle on the par-4 18th hole, McDaniel was met at his ball by Craig.
Luis Ruiz and Morgan Deneen each shot a 4-under par 68 as both carded five birdies, one bogey and 13 pars. The finish marked his eighth top 10 of the season.
Playing in his first South Carolina Senior Championship, Rich Weston of Pawleys Island was clearly the best player in the field this week. His season scoring average of 72.69 ranks 11th-best in school history while his current career scoring average of 73.82 ranks ninth.
A&M head coach, J.T Higgins said he is proud of the way his team performed and why winning on their home turf was the icing on the cake.
"We has beaten Vanderbilt earlier in the day and it was hard to come back and play an emotional match with Arkansas, who we have sort of been battling all year", Potter said. "With all four of these guys returning next season, I think we've seen just a glimpse of what the future holds for our program".
Thirty teams, five from each of the six regional sites, will now converge at Karsten Creek Golf Club in Stillwater, Okla., for the NCAA Men's Golf Championship, which will be played May 25-30.