Both teams found goalscoring opportunities hard to come by during the first half at Carrow Road.
Hosting Norwich created the only real chance of the half in the 26th minute, but Surman's effort struck the crossbar following a lay-off from captain Grant Holt.
Surman was more accurate after the break, sending Elliott Bennett's cross into the roof of Adam Bogdan's net at the second attempt with 70 minutes played.
Holt shot over from two yards as Norwich looked to make the game safe, while Tyrone Mears retreated to deny Pilkington an open goal.
Pilkington did manage to wrap up the victory five minutes from time when he reacted to a save from Bogdan to send the ball into the net from close range.