In another surprise opening day result, the Green Bay Packers slumped to a 30-22 home loss to NFC rivals the San Francisco 49ers but the New England Patriots and New York Jets made positive starts to the season with comfortable victories.
For the Redskins, 5-11 last year, the trip to the Superdome to face a New Orleans team that was fired up after the disciplinary action imposed by the league following the 'Bountygate' allegations, was a major test of their off-season upgrades and they passed in impressive style.
As well as Griffin, another Redskins rookie in running back Alfred Morris also had an outstanding debut, rushing for two touchdowns and 96 yards.
A Jimmy Graham touchdown on a 20-yard pass from Drew Brees had put the Saints 7-3 up but the first sign that Griffin had settled in perfectly came with his maiden touchdown, a smart pass down the middle to Pierre Garcon, who romped into the end zone to complete an 88-yard score.
Griffin's five-yard touchdown pass to Aldrick Robinson in the second quarter gave the Redskins a firm grip on the game.
Griffin was the second pick in this year's draft and the quarterback who was selected above him, Andrew Luck of the Indianapolis Colts, had more of mixed start to life among the professionals.
Luck, stepping into the shoes of Peyton Manning, who made his debut for the Denver Broncos later on Sunday, threw for 309 yards and a touchdown but also gave up three interceptions as the Colts fell 41-21 to the Chicago Bears.
The Bears banked a lot on teaming up quarterback Jay Cutler with wide receiver Brandon Marshall and the pairing delivered. Cutler threw for two touchdowns and 333 yards and Marshall collected one of those scores as he put up 119 yards receiving.
The Packers are among many experts' favourites to reach the Super Bowl again, after winning it two seasons ago and going 15-1 last season, but they looked far from championship material at Lambeau Field.
As with last season their defense struggled but unusually Green Bay's offense failed to compensate.
The game turned decisively towards the 49ers when Packers quarterback Aaron Rodgers threw his second interception of the game, which was picked off by linebacker NoVorro Bowman, and a play later, running-back Frank Gore powered in to make it 30-15.
James Jones collected on a Rodgers 10-yard pass to cut the lead to eight but it wasn't enough to stop Jim Harbaugh's 49ers making an early statement of intent.
While all the eyes were on Griffin and Luck, three other rookie quarterbacks had tough baptisms.
Brandon Weeden threw four interceptions (0 touchdowns, 118 yards) in the Cleveland Browns' 17-16 home loss to the Philadelphia Eagles while Miami's Ryan Tannehill threw three in a 30-10 loss at Houston.
Russell Wilson's first start for the Seattle Seahawks ended in disappointment as he threw three straight incompletions at the close as the Arizona Cardinals held firm for a 20-16 win.
While rookie signal callers can benefit from the patience granted by lower expectation, New York Jets quarterback Mark Sanchez is under pressure right from the outset this season.
The Jets' decision to bring in Tim Tebow as back-up has created intense media interest but Sunday's opener could not have gone better for the starter Sanchez.
The fourth-year quarterback threw for three touchdowns and 266 yards as New York blew away the Buffalo Bills 48-28 while Tebow played bit-part roles in a variety of positions including tight end and on kickoff returns as well as quarterback.
Super Bowl runners-up New England looked in good shape on both sides of the ball in their 34-13 win at the Tennessee Titans, with quarterback Tom Brady finding tight ends Rob Gronkowski and Aaron Hernandez with touchdown passes.
The new regular season overtime rules were used for the first time as the Minnesota Vikings beat the Jacksonville Jaguars 26-23 with Blair Walsh providing the game-winning field goal.