Bongane Ndulula opened the scoring after just four minutes before Siyabonga Nhlapho equalised in the 24th minute. And just when it looked as it Bucs would have to settle for a point, Bester smashed home the winner from 25 yards out.
Ndulula got his side off to the perfect start when he bundled Ofusu Appiah off the ball before slotting home from close range.
And the Buccaneers went on to dominate possession and waste numerous half chances throughout the first half.
It therefore came as a surprise to everyone at Orlando Stadium when Cosmos bagged an unlikely equaliser.
Nhlapho cleverly created some space for himself and rocketed a 30 yard shot into the top left corner of the net.
Thabo Matlaba came close to restoring the lead for Pirates on the stroke of half time with a powerful shot but Phali did well to get his hands on the ball and send both sides in level pegging at the break.
An even more determined Bucs side emerged for the second half while Cosmos did their utmost to stifle their opponents.
The introduction of Daine Klate for Tlou Segolela added some much needed pace but a lack of cohesion going forward in search of a winner almost proved their downfall.
The usually influential Oupa Manyisa was restricted to shots from distance and when Klaite did deliver, from a corner, Thulasizwe Mbuyane, failed to get his header on target.
Lucky Lekgwathi should also have done better with a shot with 10 minutes of the match remaining following another Klate corner.
But Bester made no mistake when he set his sights on the Cosmos goal and let rip with a thunderous effort.