Hull loanee Tom Ince was also on target for the third time in two appearances as Derby twice came from behind to earn a deserved draw.
Bournemouth appeared to have taken a giant step towards the Premier League when goals from Matt Ritchie and Callum Wilson gave them a 2-1 advantage.
But substitute Bent set up a grandstand finish, expertly taking a Simon Dawkins cross in his stride before drilling his shot past the helpless Artur Boruc from six yards.
Bournemouth showed why they are the country’s leading scorers by taking the lead with their first meaningful chance after only 12 minutes.
Wilson came bursting down the right and his cross was chested down by Yann Kermorgant for Ritchie to send a cushioned volley beyond Lee Grant and into the bottom right corner.
Derby’s misery was compounded on the 15-minute mark as top-scorer Chris Martin hobbled off to be replaced by Bent.
Wilson almost doubled the home side’s lead after seizing on a poor clearing header form Richard Keogh only to steer his shot wide from the edge of the penalty area.
It was a pulsating contest and home goalkeeper Boruc sprang into action midway through the first half to turn behind Bent’s near-post volley after a clever chip from Will Hughes had sent the ex-England striker clear.
Derby hit back on the half-hour mark after a rare poor piece of defending from Bournemouth’s usually reliable centre-back Steve Cook.
Ince finished emphatically from 12 yards after the busy Bent had robbed Cook by the corner flag and pulled back a cross.
If the heat of the promotion battle was getting to Bournemouth they certainly did not show it when Wilson restored their advantage in the final minute of the half.
Kermorgant worked tirelessly to chase a long punt up field and keep the ball in play before teeing up strike partner Wilson to thunder a right-foot shot across Grant and into the top corner.
It was an eventful half for the Derby goalkeeper who was lucky to escape referee Mark Clattenburg’s notepad in the opening minutes after inexplicably carrying the ball outside his area.
The second half was not as frenetic as the first but it required a heroic block by Bournemouth captain Tommy Elphick to deny Ince a second successive brace after the quick-fire winger wriggled past two defenders.
Bent silenced the home fans in the 67th minute – again showing Aston Villa boss Paul Lambert what he is missing by sending him on loan.