Second-half substitute Poleon lashed home a knockdown from former Bournemouth defender Jason Pearce in the 80th minute to secure Leeds their first Sky Bet Championship win in four matches.
But the manner in which Leeds halted a four-game losing sequence will surely be of concern to manager Brian McDermott as they laboured against a Bournemouth side harshly reduced to 10 men in the 31st minute.
Goalkeeper Ryan Allsop was shown a straight red card after being adjudged to have brought down Leeds striker Noel Hunt.
Replacement keeper Darryl Flahavan saved Ross McCormack's subsequent penalty and although Leeds struck through McCormack early in the second half, Bournemouth striker Lewis Grabban fired the visitors level.
Bournemouth had enjoyed a comfortable first half an hour and it was Grabban who had blazed the game's first shot over the crossbar in the 28th minute.
Leeds had been unable to muster a single effort on target when they were fortuitously offered the chance to take the lead three minutes later.
The ball ricocheted back into Hunt's path in the Bournemouth penalty area and when the Leeds striker tumbled under Allsop's sprawling dive to gather the ball, referee David Coote pointed immediately to the spot.
If that decision seemed harsh, the visiting bench looked on in dismay when Coote showed Allsop a straight red card - but Flahavan saved McCormack's spot-kick low down to his left and the rebound was hacked clear.
Leeds looked far more threatening once Bournemouth had been reduced to 10 men - midfielder Ryan Fraser was sacrificed for Flahavan - but failed to capitalise following concerted pressure in and around the visitors' box.
But the home fans did not have to wait long for Leeds to make the breakthrough.
Teenage midfielder Alex Mowatt, making an impressive home league debut, fed marauding left-back Stephen Warnock and his superb low cross was swept home from close range by McCormack in the 52nd minute.
Bournemouth were intent on getting forward when ever they could and midfielder Jack Collison, signed on loan from West Ham earlier in the day, fired a warning with a right-footed curler that Leeds keeper Paddy Kenny did well to hold.
The warning was not heeded however and Bournemouth levelled when a long free-kick was headed on by Eunan O'Kane and lashed home on the volley by Grabban in the 73rd minute.
Leeds skipper Rudy Austin was thwarted at the far post by Flahavan's one-handed save soon after, but the home side went back in front 10 minutes from time.
Mowatt's deep cross was headed back across the six-yard box by former Bournemouth defender Jason Pearce and Poleon rammed home his first league goal of the season.
Leeds, who pressed for a decisive third goal, were kept on their toes by Bournemouth in the closing stages, but saw the game out for their fourth league win of the season.