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After a quiet start to the game, it looked like the home side would have a chance to get some points on the board late in the first quarter, but Matthew Stafford had a pass intended for Golden Tate intercepted by Keenan Lewis.
Stafford handed the ball off to Joique Bell to try and get Detroit back on level terms, but they had to settle for a Matt Prater field goal, while Shayne Graham added a further three points for New Orleans just before the break.
The visitors continued to enjoy the better of the chances early in the third when Brees completed a long pass for Kenny Stills, who held on for a touchdown.
Graham added a couple more field goals in the fourth quarter to extend the Saints' lead to 13 points, but Tate found the endzone inside the final four minutes to give Detroit a chance.
It looked like Brees had managed the clock well to see out the win for the visitors, but Glover Quin intercepted the quarterback's pass to give Stafford and the Lions one final chance.
Stafford quickly got the ball downfield for Detroit before throwing a pass deep for Corey Fuller, who just kept himself in bounds at the back of the endzone, sealing the win for the home side.
The win leaves the Lions at the top of the NFC North with a 5-2 record, while the Saints slip to 2-4, leaving them second in the NFC South.