The away side had the first real chance of the game after six minutes through Pablo Hernandez, who fired a low shot just wide of the post.
Swansea then took the lead on 12 minutes after Nathan Dyer ran onto his own flick-on and lifted the ball over John Ruddy.
Two minutes later, Norwich had a penalty shout turned down after the ball struck Angel Rangel on the arm, although it looked as though there was nothing the defender could do about it.
Michu found himself in some space in the box on 24 minutes, but the forward skied his effort well over the bar.
Norwich grabbed an equaliser four minutes into injury time through Hooper, who chested the ball down and smashed a volley past Vorm.