Diggs' score came four minutes after Seth Fisher's 12-yard touchdown run, which brought Richmond back from a 28-16 deficit after the third quarter.
Lauletta was 20 of 32 for 247 yards and two touchdown passes.
Hampton built a 21-7 halftime lead on two touchdown passes from David Watford - to Twarn Mixson and Shakim Alonzo - and Mixson threw for a score. Mixson threw a 15-yard pass to Rashawn Proctor that started the scoring not two minutes into the game after Breon Key picked off Lauletta and returned it to the Richmond 15.
Watford finished 17 of 33 for 239 yards and three touchdowns.
Richmond (1-1) is 22-1 in non-conference FCS games since 2005.
Hampton (1-1) is 0-3 against their in-state rival and 2-14 all-time against Colonial Athletic Conference opponents.
AP College Football website: www.collegefootball.ap.org