Winger Chapell's 18-second shot - his fifth goal for the Gulls - was the fastest in the Devon club's history.
But substitute Ryan Bird's equaliser nine minutes from time rescued Pompey and leaves Torquay without a win in six games.
Torquay's dream start came when Karl Hawley laid Lee Mansell's header off for Chapell to score with a 10-yard left-foot shot across goalie Trevor Carson.
Torquay had problems containing Pompey targetman Patrick Agyemang, who had a great battle with home defender Krystian Pearce, while on-loan West Ham striker Paul McCallum missed a great chance, laid on by Hawley, to make it 2-0 just before half-time.
With the wind behind them, Pompey cranked up the pressure in the second half, skipper Johnny Ertl forcing Martin Rice to make a fine save and Jed Wallace firing wildly over in the 71st minute.
But the pressure finally told when Wallace crossed from the right in the 81st minute and Bird stretched out his right boot to wrong-foot Rice and poke the ball home from close range.