Tubbs spared the Cherries' blushes with a goal two minutes into injury time - the previously rock-like Hartlepool defence having been undone by a route-one goal.
With time running out and Bournemouth trailing to a 73rd-minute penalty by Simon Walton, goalkeeper Shwan Jalal lumped a desperate clearance almost the length of the field.
Hartlepool, who had defended stoutly for 90 minutes, failed to clear their lines and Wes Fogden created an opening for Tubbs to nick the equaliser.
Bournemouth's increasingly frustrated fans, yet to savour a home win this season, watched their side huff and puff their way to a third successive 1-1 Dean Court draw.
Hartlepool had been set to nick a rare win on the strength of Walton's second-half penalty, awarded for a foul by Bournemouth's Shaun MacDonald on Evan Horwood on the right-hand edge of the penalty area, but Tubbs, whose name had been chanted by the Cherries fans for over an hour, denied them in the dying moments.