GOALS either side of half-time from Brian Stock and James Hayter propelled classy Cherries onto the fringes of the League One play-off zone. (Oct 8)
Stock set the ball rolling when he despatched a stunning 20-yard free-kick into the roof of the net midway through the first half.
And Midas man Hayter plundered his ninth goal of the season with a close-range header just minutes after the break.
Cherries' convincing victory capped a miserable night for Dean Court old boy Warren Feeney whose new club remain rooted to the foot of the table.
But despite finishing up on the losing side, the Ulsterman did have the satisfaction of grabbing a late consolation for County in the closing stages.
Neil Young was restored to the Cherries starting line-up at the expense of Shaun Maher, while for County, former Dean Court favourite Feeney faced his old club.
Hayter looked to forge the first opening after giving his marker the slip near the left touchline but County goalkeeper Neil Cutler got down smartly to smother his low cross.
Hayter then got up to meet Wade Elliott's eighth-minute centre, and, although his header flew just wide of the upright, referee Steve Tomlin had already blown for a free-kick against the Cherries man.
Feeney was taunted by a section of the home fans following his late tackle on Young before Cherries supporters shouted in vain for a penalty after Danny Adams had challenged Hayter.
The visitors' first effort on target came in the 19th minute when Cherries goalkeeper Neil Moss dived to his right to save Lee Cartwright's long-range shot after Rickie Lambert's corner had only been half cleared.
But the hosts countered almost immediately when Hayter just failed to connect with Elliott's cross from the right before Cutler saved with his legs after Garreth O'Connor had pounced on the loose ball.
Cherries opened the scoring in the 22nd minute, the goal owing much to an electrifying run from Warren Cummings who created a move which ended with the Hatters defence conceding a free-kick just outside the box.
And dead-ball specialist Stock stepped forward to pick his spot and clipped a delightful effort into the top right-hand corner of Cutler's net for his second goal of the season.
Cherries thought they had won a penalty after Dani Rodrigues had taken a tumble under a challenge from Danny Jackman - but referee Tomlin had pointed for a goal kick rather than a spot kick.
County number two Mark Lillis, who had clearly jumped the gun and remonstrated too vociferously with fourth official David Phillips, was banished to the stands for his protestations.
Luke Beckett had the ball in the net for County in the 38th minute, although his strike was chalked off as the linesman had indicated the ball had already gone out of play before Derek Geary had centred.
Cherries doubled their lead fewer than three minutes into the second half when Hayter nodded home his ninth goal of the season from close range after O'Connor's shot from Elliott's cross had rebounded to him off the post.
Elliott, lively in the first half and instrumental in the second goal, looked to get on the scoresheet himself when his long-range drive cleared the crossbar as Cherries began to take a stranglehold on proceedings.
Stockport squandered a glorious chance to reduce the arrears on the hour when leading goalscorer Beckett miscued a near-post header from inside the six-yard box with the goal gaping.
But normal service was soon resumed when a low drive by Elliott was turned around the post by Cutler before Hayter headed narrowly over the crossbar from the resultant corner.
O'Connor sent a rasping effort flying inches past the upright and although Cherries dominated possession for long periods, Feeney threw County a lifeline when he netted with a looping header five minutes from time.
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