Dungey, a junior who's among the nation's top quarterbacks, completed his first 12 passes and finished 28 of 36 for 328 yards and three touchdowns. He also rushed nine times for a team-high 51 yards and two touchdowns before leaving after two series in the third quarter.
In logging his seventh career 300-yard passing game, Dungey connected with wide receiver Steve Ishmael 12 times for 134 yards.
The dynamic but injury-plagued Dungey has been unable to finish the last two seasons. Before suffering a season-ending concussion last year, Dungey set Syracuse sophomore quarterback records for passing yards (2,679) and total yards (2,972) in nine games.
On Syracuse's first three possessions, Dungey ran 11 yards for a score, running back Dontae Strickland bolted 6 yards for a touchdown and Dungey connected with wide receiver Ervin Philips for a 14-yard score.
After Cole Murphy's 29-yard field goal made it 24-0, Dungey and wide receiver Moe Neal teamed up for a 52-yard catch-and-run that boosted the Orange's lead to 31-0.
The Blue Devils opened the second half with their only score as Jake Dolegala found Jose Garcia in the corner of the end zone on a fourth-and-4 play from the Syracuse 24.
Dungey answered with a 5-yard touchdown strike to Ravian Pierce and a 2-yard touchdown keeper to increase the lead to 44-7.
The Orange, who lost their last four games of 2016 to finish 4-8, defeated a FCS school in their season opener for the fourth consecutive year.
Syracuse can be excused for scheduling Central Connecticut State this season. Each of the Orange's next 11 FBS opponents played in a bowl game last year and five of them are currently ranked in the top 20.
The Blue Devils, who finished 2-9 last season, were picked to finish fourth in the Northeast Conference.
Dolegala completed 6 of 19 passes for 86 yards and Cameron Nash picked up 35 yards on nine carries as Central Connecticut State gained only 167 yards to Syracuse's 586.
Syracuse junior safety Antwan Cordy, perhaps the team's best defensive back, limped off the field in the first quarter and returned to the sideline on crutches with his right foot in a boot. Cordy missed most of last season because of a broken forearm.