Managerless Bournemouth reached the quarter-finals of the FA Cup for the first time in 64 years with victory at Premier League Burnley.
Junior Stanislas added the second from the penalty spot after Surridge was fouled.
Bournemouth, who have won both of their games under caretaker-manager Jonathan Woodgate, were deserved winners.
On a bad night for the Clarets, they were forced to make a late change when it was pointed out that defender Erik Pieters, who was named in the starting line-up, had been booked in the previous two rounds and was therefore suspended.
Bournemouth keeper Asmir Begovic saved from Matej Vydra and Dwight McNeil, while Jay Rodriguez blazed a great chance over from close range.