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 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.
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.
- Sports & Recreation
- Karl Hawley