The top two picks in the NFL draft both threw touchdown passes in a game as they played one series into the third quarter of a game the Redskins would eventually win by a 30-17 scoreline.
Griffin hit wide receiver Santana Moss on a four-yarder to put Washington 14-7 ahead, tail-back Alfred Morris having also found the end zone for them on a two-yard run in the first quarter.
In between Luck completed a 31-yarder to fellow rookie TY Hilton to level the scores at seven apiece - the former Stanford University pupil completing 14 of his 23 pass attempts for 151 yards.
Rex Grossman replaced Griffin under centre and duly led two scoring drives that were completed by TD passes to Josh Morgan and Dezmon Briscoe. There was also a safety for the Redskins, Colts' back-up quarterback Chandler Harnish being tackled by Chris Wilson in the end zone.
Elsewhere on Saturday night, wide receiver Antonio Brown caught a pair of touchdowns to help the Pittsburgh Steelers record a 38-7 thrashing of the Buffalo Bills, who have now lost all three of their warm-up games.
Brown reeled in passes from Ben Roethlisberger and Byron Leftwich, who also hooked up with Derrick Williams for a further TD in the fourth quarter, as he finished with seven catches for 108 yards.
All this came after Fred Jackson had given the Bills the lead on a one-yard run in the first quarter. Quarterback Vince Young struggled in his efforts to clinch the back-up job for Buffalo, throwing two interceptions.
Matthew Stafford threw for 68 yards until leaving with an injury to his non-throwing hand in the Detroit Lions' 31-20 loss to the Oakland Raiders.
The quarterback - who was hurt in the second quarter after being tackled by defensive end Dave Tollefson - was not the only Lion left licking his wounds, with cornerbacks Bill Bentley and Chris Houston and running back Kevin Smith also forced out of the action.
The Raiders trailed 13-10 until back-up quarterback Terrelle Pryor took charge of proceedings, throwing touchdown passes of 39 and 76 yards as well as scoring himself on a 17-yard run.
Tony Romo and Dwayne Harris combined for two touchdowns as the Dallas Cowboys saw off the St Louis Rams 20-19, while Drew Brees was in excellent form as the New Orleans Saints triumphed 34-27 against the Houston Texans.