Smith smashed home from 15 yards in the 89th minute, soon after Pompey sub Danny Rose scored a 25-yard screamer in off the underside of the bar.
Plymouth's Yann Songo'o stooped to head the leaders ahead on 20 minutes, converting Graham Carey's inswinging free-kick from the left touchline at the near post.
Argyle should have doubled their lead in the next attack but Jordan Slew's close-range shot was scrambled off the goal-line by Carl Baker.
Portsmouth levelled when Conor Chaplin swept past Nauris Bulvitis down the left and teed up unmarked Kyle Bennett, who roofed in a rising first-timer from just inside the box.
Paul Cook's side started the 100th dockyard derby brightly and Argyle's opener came against the run of play.
Carey came closest to scoring midway through second half, beating Portsmouth keeper David Forde with a dipping 20-yarder that came back off the face of the crossbar.