Cheltenham warmed up for the play-offs, ending a run of six straight away defeats.
Former Argyle striker Steve MacLean, on loan from Yeovil, came back to haunt the Home Park faithful with the first goal.
The Pilgrims equalised in the 54th minute through half-time sub Juvhel Tsoumou, but the Robins regained the lead a minute later. MacLean crossing for Marlon Pack to head in.
Cheltenham will face Argyle's Devon rivals Torquay in the play-offs.