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.
College football best of Week 11: Top 25, scores, picks, betting tips and highlights
Highlights, analysis and all the biggest news of the weekend.
Tebow: Terrell Lewis could be a key to Alabama's win
Tim Tebow breaks down how Alabama can stop Joe Burrow and how linebacker Terrell Lewis could play a key role for the Crimson Tide.
Ahmed has 2 TDs and Washington downs Oregon State 19-7
Salvon Ahmed ran for a career-high 174 yards and two touchdowns, and Washington rebounded from a two-game losing streak with a 19-7 victory over the Oregon State Beavers on Friday night.
Rainey FG, 4th-down stop lift Tulsa over UCF 34-31
Jacob Rainey kicked a 23-yard game-winning field goal late in the fourth quarter and Tulsa rallied past UCF, knocking off the two-time defending American Athletic Conference champs 34-31 Friday night.
Things get heated between UCF teammates
Tempers begin to flare for UCF as teammates Kenny Turnier and Nate Evans engage in a heated confrontation.
Does Florida need to be dominant vs. Vandy?
SEC Now analyst Chris Doering talks Florida-Vanderbilt and what the Gators need to do moving forward.