"It was one of those days you don't get wrapped up in the score because it was playing so difficult," Hossler told the Golf Channel.
"My short game kept me in it. And at the end of the day, I had a nice round."
Spaun had a more challenging third round with three bogeys in his first five holes and another at the 17th leaving him with a two-over 73 and a share of the lead.
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The 27-year-old was three clear of the field when bad light prematurely ended the second day's play but will now be on level pegging with Hossler on Sunday as they battle it out for what would be a maiden PGA Tour victory for both.
"The biggest accomplishment is still having a shot tomorrow to win the tournament. That's all I can ask for," Spaun said.
"It was a matter of keeping things together. To not fall off coming in helps me have confidence for tomorrow."
Spaun and Hossler are three clear of compatriot Tony Finau, who shot a 69 for third place. Four players were in a share of fourth at five-under.
Hossler came into the spotlight back in 2012 when he qualified for the U.S. Open at the age of 17 and finished tied for 29th. He turned professional in 2016 and last week in Mississippi recorded his first top-10 finish in 14 starts.
(Reporting by Jahmal Corner, editing by Nick Mulvenney)
