"I've tried to learn not to make too much out of a single game either way, but no question this advances our journey a bit," Freeze said. "To be where we're sitting here year one far surpasses certainly the prognosticators and whatever they had for us. Our guys really chose to buy in and determine we could be who we want to be. We don't have to have someone else determine that."
The bowl win was especially satisfying for veteran players who had no postseason last year.
"The best thing is our program is moving in the right direction," said junior linebacker Mike Marry, who had four of the Rebels' 11 tackles for losses. "We're not where we want to be right now but we're moving there."
Freeze's no-huddle, up-tempo offense produced 38 first downs and 387 yards. Pitt was held to 266 yards, its second-lowest total of the season.
"Obviously, it was a tough one for us," said Pitt coach Paul Chryst, also completing his first season. "Give Ole Miss credit. They beat us in almost every phase. They were clearly the better team."
Wallace, chosen the game's MVP, completed 22 of 32 passes for 151 yards with three touchdowns and two interceptions. He judged his performance as only average.
"I played OK. Nothing just crazy," Wallace said. "I felt really good at the start of the game and then had the two interceptions and just had to bounce back from it."
Pitt (6-7) struggled on offense as leading rusher Ray Graham was held out with a hamstring injury he suffered in bowl practice.
"We just couldn't get in a rhythm, probably because of their pressure," said Pitt wide receiver Mike Shanahan, who had a 16-yard touchdown catch in the fourth quarter.
"We just couldn't seem to get in good field position."
The Panthers fell behind in the opening minutes after quarterback Tino Sunseri threw his first interception since Sept. 15 and trailed the remainder of the game.
Wallace's 13-yard touchdown pass to Ja-Mess Logan gave the Rebels the 7-0 lead. Wallace added first-half touchdown passes to Randall Mackey, for 27 yards, and Vince Sanders, for 18 yards.
Pitt was making its third straight appearance in the bowl. The Panthers lost to SMU in last year's game.
The Panthers played their last game as a Big East team. They are moving to the Atlantic Coast Conference next season.
Ole Miss backup quarterback Barry Brunetti had a 1-yard touchdown run in the third quarter and freshman running back I'Tavius Mathers added a 62-yard scoring run midway through the fourth quarter.
Pitt stayed close early with Devin Street's 10-yard pass from Sunseri in the second quarter. That was Pitt's only touchdown until Sunseri's scoring pass to Shanahan with only 2:23 remaining.
Sunseri completed 16 of 32 passes for 185 yards with two touchdowns and one interception. Ole Miss had four sacks.
Pitt had only one turnover in its last seven games of the regular season. It shared the nation's lead with only eight turnovers for the season.
Sunseri's streak of 271 passes without an interception, the nation's longest, ended on his second throw of the Panthers' opening drive. Senquez Golson's interception, returned 17 yards to the Pitt 23, set up Wallace's touchdown pass to Logan. It was only Sunseri's third interception of the season and his first since the team's third game against Virginia Tech.
Sunseri lost a fumble early in the second quarter for the Panthers' second turnover.
Wallace completed his first eight passes, including two for touchdowns but his hot streak ended with two second-quarter interceptions.
Kevin Harper kicked a 47-yard field goal, his longest of the season, for Pitt in the second quarter. Bryson Rose kicked a 31-yard field goal for Ole Miss and missed from 44 and 48 yards.
Pitt said Graham, the team leader with 1,042 yards rushing, suffered the hamstring injury in bowl practice.
Rushel Shell and freshman Malcolm Crockett, who had only 32 yards rushing in the regular season, shared the carries. Shell led the Panthers with 25 carries for 79 yards. Crockett added five carries for 18 yards.
Freeze said a hamstring injury in the game limited Ole Miss starting running back Jeff Scott to five carries for 16 yards.
Mathers led the Rebels with 96 yards rushing on only six carries. Jaylen Walton had 10 carries for 56 yards.
A strong turnout by Ole Miss fans within driving range of Birmingham pushed attendance to 59,135, easily a bowl record. The previous high was 42,610 for the 2010 game between South Carolina and Connecticut.