Savage's hosts ran out 3-2 winners against James Collins' youngsters in Wolves' second group B fixture.
Strict competition rules state fifth tier National League clubs must include at least four players who started the club's previous fixture in their first XI.
With managers keen on wholesale changes to rest players for league endeavours, former Premier League midfielder and Wales international Savage found a way to rest all his players while staying within guidelines.
His hosts instead opted to make four substitutions inside a minute of the cup tie at Rovers' New Lawn home.
Forest Green forward Tom Knowles, winger Kyle McAllister, left-back Neil Kengni and centre-back Abraham Kanu all remained in the starting line-up, but Savage replaced them all with fringe players just seconds after kick-off.
Wolves under-21s fell to their second defeat in two in the competition with the 3-2 defeat. Striker Mateus Mane briefly drew the visitors level after half-time in Gloucestershire but the home side went 3-1 up before Dani Angel's last consolation.
Rovers, who are expected to battle for promotion to League Two, were not the only club to sneak around the rules of the controversial competition, as league rivals Rochdale did likewise with two early changes in a 3-2 victory over a Blackburn youth side.
The National League Cup, in its second season, sees clubs from the fifth tier compete with academy under-21 sides from the Premier League and Championship.
The new competition has come under fire from some National League clubs and its supporters, who do not feel their side should be in action against youth opposition.
Savage, who took charge of the non-league side in July, has overseen an unbeaten start to life at Forest Green. His side sit second after six wins and three draws in the league, behind Rochdale on goal difference.