Pack drilled a low shot beyond goalkeeper Conrad Logan on 11 minutes to cap an impressive display.
The Robins should have added to their tally before half-time with Luke Garbutt forcing Logan into a hurried save when he let fly with a 35-yard effort.
After a promising opening 10 minutes, Rotherham struggled to create anything of note before the break, Lewis Grabban going closest when he dragged a shot wide after holding off defender Steve Elliott.
The Robins continued to dominate the chances after the break with Jimmy Spencer hitting the outside of the post midway through the half before substitute Kaid Mohamed, on the pitch for less than a minute, was denied by a full-length save.
Cheltenham keeper Scott Brown was finally forced into action late on to keep out a Brett Williams header but the home side ran out worthy winners.