Blair Riley gave the Giants the lead on the powerplay in the first period and Brandon Benedict increased their advantage, again on the powerplay.
Alex Nikiforuk pulled one back but Jim Vandermeer's goal made it 3-2 to the Giants at the end of the second period.
Brad Moran was on target for Nottingham but Michael Forney replied for Belfast.
Jackson Whistle began the game as netminder and was named as the Giants' man of the match after facing 26 shots in helping his side to victory.
The Giants' next Elite League match is against Fife Flyers at the SSE Arena on Friday night, followed by another home fixture against Cardiff Devils on Saturday.
The Belfast Giants bounced back from their 4-1 defeat by Coventry Blaze on Saturday as they beat Nottingham Panthers 4-2 away from home on Sunday.