That miss came back to haunt the Seagulls when Matt Ritchie put the home team ahead just moments later, finding the net with a direct free kick from 20 yards.
Ritchie could have doubled his tally minutes later had Kuszczak not been alert to his header after Ryan Fraser had sent in a good cross from the left.
Pitman missed a good chance to make it 2-0 to Bournemouth in the opening minutes of the second half when he was sent through on goal by Ritchie, but his shot was turned away by Kuszczak.
Then on 55 minutes Brighton restored parity. A throw-in found Barnes with his back to goal on the right side of the area; he juggled the ball and slammed home a half-volley with his left foot.
Pitman could have put his side ahead again in the 73rd minute, but he dragged his shot wide from a good position.