Although fans were not allowed into the Allegiant Stadium for the first match since the team's move from Oakland, the Raiders began their new life in style as they overcame an early 10-point deficit.
Quarterback Derek Carr led the way, throwing three touchdown passes to calmly engineer his side's fightback, which took them to 2-0 for the season.
He completed 28 of 38 passes for 282 yards, with Darren Waller catching 12 of them to gain 103 yards.
After New Orleans led 10-0 at the end of the first quarter, the Raiders got back into the match and had drawn level at 17-17 by half-time, before taking the lead in the third quarter.
The Saints reduced the deficit to 31-24 in the closing stages to give their fans hope, but the Raiders managed to secure the result through a 54-yard field-goal to Daniel Carlson.