Hossler is No.122 in the FedEx Cup, knowing his only mathematical chance to be among the top 70 to advance to playoffs is to win for the first time on the PGA Tour.
Brennan, who went from the PGA Tour Americas to a PGA Tour card by winning the Bank of Utah Championship last autumn, made a birdie putt from 15 feet on the last hole for a 63.
They were at 16 under 194, one shot ahead of Scottish Open winner Tom Kim (63) and two clear of Alex Noren and Alex Smalley, who each shot 65.
Such is the nature of the final regular-season tournament -and the stakes - that nine of the top 10 players on the leaderboard shot 66 or lower on Saturday.
Hossler was leading until a 30-minute delay because of storms, and returned to three-putt from 30 feet for bogey on the par-3 16th, ending his streak of 31 holes without a bogey. He hit his tee shot into the rough on the 17th and then came another delay of 1 hour, 20 minutes.
The rough was even thicker and damper when he returned, and the greens were as challenging as ever. Hossler saved par with three putts from 10 feet or longer, and three others in the 5-foot range.
"That might be the hardest two-putt on the PGA Tour right there," Hossler said of the 18th green.
Englishman Jordan Smith, No.68 in the FedEx Cup standings, helped his cause in many ways when he made a hole-in-one on the par-3 16th with a nine-iron. His ace also came with a million reward points from tournament sponsor Wyndham. Smith is tied for eighth at 11 under.
Davis Thompson had enough drama to last a week. He is at No.81 - a year ago he finished 71st after the Wyndham Championship and missed the post-season by five points - and holed out with an eight-iron from 186 yards for an albatross on the par-5 fifth.
The other par-5 at Sedgefield didn't work out as well. Thompson noticed a crack in his driver on the 13th hole, and had a spare driver head in his locker. But before it could be brought out to him, he reached the par-5 15h and had to hit three-wood. He hit three-iron into the bunker and had to settle for par.
Even so, his 65 put him in a great spot to hold his own and advance to the post-season.
Hossler has no choice but to win if he wants to get into the lucrative post-season, which starts with a pair of $US20 million tournaments.
Brennan, at No.105, could finish in a three-way tie for second and still have a mathematical chance at the top 70.
