Ginn was able to get open on a shallow cross out of a bunch set in the first quarter, easily avoided a tackle attempt from rookie LB Jarrad Davis, and dove into the end zone for a 20-yard score.
But Detroit scored 28 consecutive points over the next 16 minutes to cut the deficit to 45-38 with 6:41 remaining. Stafford ended the day throwing for 312 yards for three touchdowns and three interceptions.
After the Saints again failed to pick up a first down, punter Thomas Morstead backed up the Lions at their 1-yard line.
New Orleans' defense has been the bane of the team in recent seasons - historically bad, but Dennis Allen's unit looked like the real deal in the 52-38 win over Detroit.
The Saints came right back when Cameron Jordan pulled in a batted Stafford pass in the end zone for a touchdown and a 52-38 advantage with 4:58 showing on the clock, a score that ultimately held up until the final gun sounded.
In the first game since trading Adrian Peterson, Saints running backs Mark Ingram and Alvin Kamara largely carried the offense.
Detroit quickly tied up the score on a 45-yard scoring strike from Stafford to Golden Tate, who raced down the right sideline while breaking multiple tackles with 7:02 left in the first period. Ingram had 25 carries for 114 yards, five catches for 36 yards and two touchdowns. The Saints entered the game as one of only three teams in National Football League history not to commit a turnover in the first four games, but committed two interceptions and lost one fumble.
Stafford is completing 64.2 percent of his passes for 1,116 yards through five games and has thrown nine touchdowns to one interception.
After the disappointing loss in New Orleans, the 3-3 Detroit Lions now head into their bye week.