United central defender Aaron Downes crashed home an 82nd-minute opener from Kevin Nicholson's inswinging corner from the left.
Argyle's luck looked to be out when United keeper Michael Poke went full stretch to keep out Robbie Williams' rising drive, but 17-year-old debutant Tyler Harvey had other ideas.
When the ball spilled to the teenage striker on the edge of the box he drilled it past the diving Poke to send the Green Army in a 10,003 crowd into raptures.
Ling said: "We got the goal and then had a couple of half chances and then Ashley Yeoman put across a good ball to Danny Stevens that may have killed it off.
"If I am totally honest - and even though the late goal kills you - if you look at all the play and possession then a draw is a fair result."