Paul Ince's visitors had been the better side but were unable to turn slight superiority into a winning goal as the spoils were shared .
Charlton, unchanged from the side that had drawn 1-1 at home to Nottingham Forest on Tuesday, started strongly and Dale Stephens curled an early free-kick just over the bar.
Stephens had another go soon afterwards, this time from open play and further out, but the result was another Blackpool goal-kick.
Tom Ince, the manager's highly-rated son, had a go from distance for the visitors but his shot looped up off a defender to give goalkeeper Ben Hamer an easy catch.
Referee Keith Hill turned down a Blackpool appeal on the edge of the Charlton box when Richard Wood appeared to use an arm.
Stephen Dobbie then blasted a volley over as Blackpool began to look more and more dangerous, with a deflected Ince effort winning them a corner.
Dobbie had two more attempts, firing the first wide and winning a corner with the second, but Charlton cleared before replying with a move that saw Simon Church fail to find a team-mate with a ball across the Blackpool box.
Broadfoot was booked for one foul too many before Fuller's header from an enormous throw-in from Jack Robinson was saved by the diving Hamer just before the break.
Stephens fouled Fuller shortly after the restart to put Charlton under pressure again and Ince's free-kick was deflected narrowly behind.
Ince's ball into the box had Charlton in a panic but Broadfoot went in with studs up and was punished.
The Addicks were finding chances hard to come by at the other end but Callum Harriott headed a passable one wide after the hour-mark.
The home side then had Jordan Cousins to thank for blocking a Dobbie effort at the expense of a corner.
Cousins almost fired Charlton ahead with a rasping 25-yard drive that Blackpool goalkeeper Matt Gilks did well to tip round his left-hand post.
Wood was on the end of the resulting corner but his header went just over to end Charlton's best spell of the game by far.
Blackpool sent on Dan Gosling, the midfielder signed on loan from Newcastle, for a debut and the substitute fired a long-range effort wide.
Ince burst through in the final minute but spurned a great chance to win the game by firing across goal and wide.
- Sports & Recreation
- Paul Ince
- Tom Ince
- Kirk Broadfoot