Fletcher claimed the 99th and 100th league goals of his career to add to strike-partner Goulding's double and condemn play-off hopefuls Bradford City, who scored a consolation through Matt Clarke, to a fifth consecutive defeat away from home.
Bradford's failure to cope with the raw power of Fletcher was evident from as early as the fourth minute when the Bantams back-four failed to clear and Goulding toe-ended a pass into the striker's path to place a drive past the outstretched arm of Rhys Evans.
The away side managed to draw level when Nicky Law's inswinging free-kick found the onrushing head of Clarke but it was a brief respite and the remainder of the contest belonged to Bournemouth.
The home side thought they had a second when Brett Pitman's 30th-minute corner flew straight past Evans but Fletcher was adjudged to have fouled the Bradford keeper.
But 19 minutes later Bournemouth had their second with Lee Bradbury and Mark Molesley exchanging passes down the right wing before the Cherries midfielder's dummy afforded him space to pick out the run of Fletcher to notch up a century of league goals.
Bradford's miserable first half was compounded 60 seconds later as more defensive indecision on the halfway line allowed Fletcher to send Goulding clear and plant his strike under Evans for his first goal since September.
Six minutes into the second period the game was over with Fletcher helping the ball on to Goulding and yet again the striker showed a clean pair of heels before firing inside the near post.
Michael Boulding's well-struck half-volley rattled the outside of Shwan Jalal's upright but chances for the Bantams were few and far between as Bournemouth's post-Christmas revival continued.