Stafford, who was limited to just three games last season because of a shoulder injury, capped the opening drive of the game with a 26-yard scoring strike to Calvin Johnson.
The Bengals fumbled the ensuing kickoff, and the former No. 1 overall pick hit Nate Burleson on a fourth down play from the seven-yard line to put the Lions up 14-0.
In two series, Stafford completed 6-of-7 passes for 71 yards.
Andy Dalton's pro career got off to an unsettling start as the former TCU star's first pass was picked off. He wound up playing the entire first half for the Bengals, throwing for 69 yards on 11-of-15 efficiency.
Cincinnati has turned the offense over to Dalton, who was selected in the second round of this past April's draft, after Carson Palmer opted to retire once his trade request was not granted.