Pollard scored only nine after taking one wicket as Queensland scored 156 for four off their 20 overs and South Australia replied with 160 for six off 19 overs at the Adelaide Oval.
The Pakistani all-rounder Shahid Afridi was the star performer as the South Australia Redbacks surged to their second win in as many games.
James Hopes (63) and Andrew Symonds (27 not out) were the principal scorers for Queensland while Afridi produced a four-over spell that conceded just 25 runs while claiming the vital wicket of Hopes.
The Australian Hopes had been threatening, compiling his 63 off just 45 balls with six fours and one six before he was bowled by Afridi at 130 for four in the 17th over.
Pollard bowled just one over and picked up one for 10 for South Australia, who had beaten Western Australia in their opening game last Tuesday.
Set 157 to win, South Australia got good contributions from Mark Cosgrove (43 not out), Daniel Harris (34) and man of the match Afridi (27) in securing the victory with an over to spare in front of a capacity crowd of 17,500.
Cosgrove faced 40 balls in his top score, which contained five boundaries. Pollard scored nine off seven balls with one boundary, a lofted shot off pacer Hopes down to the long-off boundary.
Pollard departed in the next over, caught on the boundary attempting a similar shot against the off-spinner Chris Simpson. The tournament continues tomorrow with defending champions New South Wales (NSW) and their West Indian all-rounder Dwayne Smith facing Western Australia in Perth.
Western Australia are expected to have West Indies captain Chris Gayle after a side strain had ruled him out of Friday’s match which they lost to Tasmania.
South Australia and Victoria lead the standings with four points each, followed by NSW and Tasmania with two each.
Queensland and Western Australia are both winless from two games.
