Torquay started brightly with Danny Stevens sending a shot spiralling over the top in the 30th minute.
Nicky Wroe tried his luck with a 30-yard grass-cutter before visiting skipper Ryan Garry glanced a header just past the far post.
But in the 49th minute, Bournemouth's Brett Pitman struck from close range, powerfully heading home Liam Feeney's cross from the left.
But United kept pressing and equalised after 64 minutes as Stevens crossed from the left for central defender Chris Todd to send a powerful point-blank header past Shwan Jalal.
Torquay's Tim Sills saw a header crash off the crossbar late on before Fletcher headed home Feeney's cross from the right to make it 2-1 in the 87th minute.