The top six in the heat qualified for the final automatically, a feat which Bleasdale achieved by finishing in fourth place.
Veteran Pavey could only manage to finish seventh, but she got through as a fastest loser.
However, there was not such good news for fellow Brit Barbara Parker, who finished ninth in the opening heat.
Following the conclusion of final race, Parker's time of 15:12.81 was not quick enough to see her advance.
The final will be run on Friday night.