The visitors forced a number of early corners, the closest of which saw defender Michael Jackson head over.
The game burst into life with half-time approaching when striker Robbie Blake teased the Blackpool defence and fed McCann whose shot cannoned back off the crossbar with goalkeeper Paul Rachubka well beaten.
At the other end Wes Hoolahan supplied a defence-splitting pass to Keigan Parker whose first attempt was blocked by a desperate challenge from Clarke Carlisle before the rebound fell kindly to Parker whose second attempt was turned behind for a corner by goalkeeper Brian Jensen.
The half finished with Blake firing over a cross from Elliott.
McCann was again involved in the thick of the action early in the second half heading over another Elliott cross from inside the six-yard box.
The Clarets went in front seven minutes into the second half when substitute Steve Jones took a return pass from Blake to score with a shot that took a big deflection on its way past Rachubka.
Blackpool's first equaliser arrived via the penalty spot after Morrell was brought down by Carlisle and Hoolahan scored with ease, sending Jensen the wrong way with his kick.
Burnley appeared to have secured all three points when another substitute, Ade Akinbiyi, held off defender Jackson and scored with a shot on the turn after more good approach play from McCann.
But Blackpool's team spirit never let them down and the Seasiders equalised for the second time when goalkeeper Jensen dropped a cross and, after Ian Evatt had missed with the first opportunity, Morrell stroked the ball home for the equaliser.