The teams finished goalless after 90 minutes in which the hosts had been the dominant force.
But when it came to spot-kicks, Bournemouth endured a nightmare with Warren Cummings shooting a yard wide, Lee Bradbury hitting a post, and Marc Pugh having his shot saved. Torquay’s penalty-takers, Chris Robertson, Nicky Wroe and Kevin Nicholson made no mistake.
Bournemouth could look back on a night of missed opportunities with Torquay goalkeeper Scott Bevan making some important saves. Bevan reserved his best for the 47th minute with a double save from Pugh and Harry Arter.
Bevan also saved with his legs from Arter as Bournemouth forced numerous corners without making the breakthrough.
League Two leaders Torquay’s best chance came in the 80th minute when Chris Zebroski had a left-foot shot turned to safety by goalkeeper Shwan Jalal.