Sharks replacement fly-half Butch James sealed an 18-16 win against the Bulls with a 79th-minute penalty at Loftus.
A Francois Venter try in the second half proved to be the only five-pointer of the match and put the Bulls in front for the first time, with Pollard and James trading penalties until the veteran struck the winning blow in the closing stages.
The Sharks were down to 14 men at two stages in the match as experiences flankers Jacques Botes and Jean Deysel both spent time on the sidelines, the Bulls capitalising in the scrum but misfiring with their lineout.
Rising star Fred Zeilinga was wayward with the boots in the opening ten minutes as the Sharks built considerable pressure in the Bulls 22, his two early shots at goal hardly the most taxing but the first sailed wide and the second attempt cannoned back off the post.
Zeilinga made it third time lucky though with his next strike, converting from in front of the posts as the Sharks took a 3-0 lead.
Their early territorial kicking game through Zeilinga and Cobus Reinach worked to great effect as Jean Deysel made key turnovers at the breakdown, the Bulls struggling to get out of their own half despite some impressive kicking from HandrÃ© Pollard.
A tightly-fought contest hinged on success at the set-piece, with the Bulls faltering at key moments through some questionable throwing from Mbongeni Mbonambi.
The Bulls scrum was in the ascendancy and after Jacques Botes was sin-binned for not rolling away in the tackle towards the end of the first half they made their numerical advantage count.
Pollard kicked two penalties and missed a speculative long-range effort having earlier rejected the chance to go for goal from a much easier distance.
Zeilinga's three penalties to Pollard's two meant that it was the visitors who lead at the interval 9-6.
A superb start from the Sharks after the break saw them add another three points despite being a man down, Deysel carrying effectively but stopped just short of the line.
For all of the Bulls' power in the scrum their lineout continued to splutter, momentum in the set-piece then turning as the Sharks defended a key scrum five metres from their own line by winning a penalty.
It was a typical example of the scrap between the two packs of forwards as the wingers were left out in the cold - one prime concern for the Bulls being their alarming number of turnovers as Deysel made a nuisance of himself at the breakdown.
In the end his activity in that area proved costly as the openside was sent to the bin, the Bulls capitalising with the try from Venter in the 61st minute.
With the Sharks now trailing for the first time in the match at 13-12 their night was made more difficult when replacement scrum-half Charl Macleod was penalised for stamping on the hand of a Bulls player at the ruck, to sacrifice a key attacking position.
The Bulls made them pay by charging up the field and winning another penalty through a punishing maul that charged into the Sharks half, Pollard converting for a 16-12 lead with time running out.
Macleod came close with a sniping break to the keep the Bulls on their toes, but the ball was lost forward as he tried to round Akona Ndungane.
Butch James added a penalty off the bench to narrow the gap to just a single point with time running out in the second half.
James then stepped up again to seal the win with only a minute left, as the Sharks continued their impressive form in this year's competition.
For Blue Bulls:
Pens: Pollard 2
Pens: Zeilinga 4, James 2
Yellow Cards: Botes, Deysel
Blue Bulls: 15 Jurgen Visser, 14 Akona Ndungane, 13 William Small-Smith, 12 Francois Venter, 11 Bjorn Basson, 10 HandrÃ© Pollard, 9 Rudy Paige, 8 Jono Ross (c), 7 Jacques du Plessis, 6 Wiaan Liebenberg, 5 David Bulbring, 4 Paul Willemse, 3 Frik Kirsten, 2 Mbongeni Mbonambi, 1 Marcel van der Merwe.
Replacements: 16 Bandise Maku, 17 Dean Greyling, 18 Grant Hattingh, 19 Jacques Engelbrecht, 20 Lohan Jacobs, 21 Ulrich Beyers, 22 Sampie Mastriet.
The Sharks: 15 SP Marais, 14 Odwa Ndungane, 13 Tim Whitehead, 12 Heimar Williams, 11 Lwazi Mvovo, 10 Fred Zeilinga, 9 Cobus Reinach, 8 Keegan Daniel (capt), 7 Jean Deysel, 6 Jacques Botes, 5 Stephan Lewies, 4 Peet Marais, 3 Wiehahn Herbst, 2 Kyle Cooper, 1 Dale Chadwick.
Replacements: 16 Monde Hadebe, 17 Danie Mienie, 18 Edwin Hewitt, 19 Marcell Coetzee, 20 Charl McLeod, 21 Butch James, 22 Louis Ludik.
Referee: Marius van der Westhuizen