The Bears, who have started the season 2-0 for the first time since 2010, scored three fourth-quarter touchdowns last week to come from behind and beat Western Kentucky 35-28.
"Our guys showed so much resilience. Second week in a row on the road," second-year coach Nathan Brown said.
Logan Birchfield booted field goals of 32 and 27 yards to give Austin Peay a 16-10 lead early in the fourth quarter. Five plays later, Smith hit Winningham with a 43-yard touchdown toss to go ahead 17-16. The Smith-to-Winningham combination worked again on an 18-yard scoring play to seal the win with 1:46 remaining in the game.
Smith threw for 283 yards and three touchdowns with Winningham hauling in eight receptions for 136 yards. Tyler Hudson had 120 yards receiving and a score on four catches.
Craig threw for 185 yards and one score with one interception for the Governors (1-1).
Central Arkansas jumps into Southland Conference play by hosting Abilene Christian next Saturday. Austin Peay will remain out of conference at Mercer.
Michigan State's Bridges entering transfer portal
Michigan State wide receiver Weston Bridges is entering the transfer portal.
Orgeron pinpoints difference maker for LSU this season
LSU head coach Ed Orgeron joins Thinking Out Loud and says the difference this year is quarterback Joe Burrow.
Does Florida have a chance to win the SEC East?
Jacob Hester joins SEC This Morning to rate Florida's chances of making it to the SEC Championship game.
Washington Huskies' MJ Tafisi suffered stinger in win over Arizona Wildcats
There is no timeline for Washington linebacker MJ Tafisi to return to action after he suffered a "significant" stinger Saturday, coach Chris Petersen said Monday.
Tennessee prepares for road matchup vs No. 1 Alabama
Head coaches Jeremy Pruitt and Nick Saban give their respective take on the upcoming Alabama-Tennessee contest.
Smart bracing for unique challenge with Bowden Jr.
Head coaches Mark Stoops and Kirby Smart discuss the Kentucky-Georgia matchup and the unique skills of the opposing QBs.