The Cherries scored with their first real attack on goal in the 11th minute after good work by striker Steve Fletcher.
After a 50-yard cross-field ball to Wade Elliott, Fletcher headed the midfielder's centre back to Gareth O'Connor who made no mistake from eight yards with a powerful right-footed shot.
Fletcher and Elliott continued to be a thorn in Wednesday's side in the first half and again combined 15 minutes before the break.
Fletcher sent Elliott free down the right and his low cross found top scorer James Hayter six yards out, only for his poked effort to go wide of the left hand post.
Wednesday's on loan striker Kenwyne Jones showed his potential after the break in his final game before returning to Southampton.
After 48 minutes Jones turned his marker Karl Broadhurst to fire a left foot shot from the edge of the box just wide.
Three minutes later following John Paul McGovern's right wing cross, Jones rose highest in the box only to see another effort go inches wide of the post.
Bournemouth had chances to double their advantage and Elliott was guilty after 58 minutes when he shot tamely at David Lucas after being put through by Fletcher.
Home keeper Neil Moss then produced an outstanding save to keep his side on level terms on the hour.
Striker Steven MacLean found space in the box and his low right-foot shot was somehow palmed away by the diving Moss.
Midfielder Marcus Browning headed a Warren Cummings free-kick wide before Wednesday's smash and grab antics in injury time.
The visitors forced a corner which was taken by Chris Brunt and Heckingbottom rose highest to head home and earn his side a point.