Shots striker Craig Reid completed his quick-fire hat-trick in the 47th minute after steering in Alex Rodman's free-kick in the 28th minute and dispatching from the penalty spot just shy of 10 minutes later.
But Torquay completed a remarkable recovery and it was target man Rene Howe who smashed in the 89th-minute winner to take his season's tally to seven after second-half goals from Billy Bodin, Ryan Jarvis and fellow substitute Ashley Yeoman.
After a remarkable night, Ling said: "After so many draws this was an incredible comeback and you have got to give credit to the players - and the character in that dressing room.
"I have never been manager of a side that has come back from 3-0 down to win 4-3 and all I can say is that it shows the character in the dressing room. Unbelievable.
"At half-time we said that the next goal would be important and we went 3-0 down within a couple of minutes."
