A goal in each half from Lee Hughes had looked to be enough for County to earn a fifth consecutive victory, only for substitute Goulding to volley in late on.
Despite losing three of their last four away games, it was the Cherries who started brightly and Anton Robinson saw his drive held early on and John Thompson hacked Alan Connell's effort off the line.
But County took the lead when Rhoys Wiggins felled Ben Davies in the box after 22 minutes and Hughes saw his tame penalty parried by Shwan Jalal only to fire in the follow-up.
It should have been 2-0 at half-time when Davies had his chip wrongly ruled out for offside and Bournemouth took advantage by restoring parity after 50 minutes, leading goalscorer Brett Pitman's pinpoint free-kick deceiving Kasper Schmeichel to find the bottom corner.
However, Bournemouth's joy was short-lived as a sweeping Davies delivery was converted at the far post by Hughes for his 26th goal of the season. In a frenetic finale, after seeing Pitman's diving header palmed to safety, County thought they had clung onto victory only to be denied by Goulding.