Midfielder Pack headed Town's 56th-minute second after Plymouth substitute Juvhel Tsoumou had levelled.
Former Argyle striker Steve MacLean fired the visitors ahead from a 23rd-minute free-kick, with the ball wrong-footing home goalkeeper Jake Cole after taking a deflection off the end of the defensive wall.
Plymouth boss Carl Fletcher made a double substitution at the start of the second half and was rewarded when on-loan Preston striker Tsoumou headed home in the 55th minute.
Town goalkeeper Scott Brown saved a header from Ladjie Soukouna and when the ball came back out to the left, Onismor Bhasera crossed for Tsoumou to score.
From the restart, Cheltenham attacked and Jermaine McGlashan's angled shot from the right was well saved by Cole, but MacLean collected the ball and crossed to the far post where Pack headed down and in.