Riddick ran for 107 yards on 19 carries and Atkinson gained 99 yards on nine rushes in the season opener for both teams.
Everett Golson completed 12-of-18 passes for 144 yards and a touchdown for the Irish, who scored on their opening drive and never looked back.
Notre Dame (1-0) led 27-3 at halftime and racked up 490 total yards to Navy's 341.
The Midshipmen (0-1) were able to trim Notre Dame's lead to 27-10 on a 25-yard touchdown pass from Trey Miller to Shawn Lynch, but could get no closer.
Miller finished the day with 192 passing yards. Lynch caught four passes for 87 yards.