Roared on by their fired-up capacity crowd, Blues made a lively start.
Koji Myoshi twice tested Norwich keeper Angus Gunn, the first of which needed a fingertip save, while Paik was halted at close range and Keshi Anderson twice had efforts charged down.
Blues keeper John Ruddy had to be alert to deny Marcelino Nunez at his near post.
It was the hosts who came closest to scoring just before the break when Gunn had to go full length to his left to keep out a dangerous ricochet off Krystian Bielik.
But 10 minutes into the second half Blues finally had lift-off when Anderson cut inside on the left corner of the Norwich box, his right-foot cross deflected kindly and Paik took his chance well, cleverly readjusting to head home from eight yards.
Blues were a goal up but home fans already knew two of their three rivals – Sheffield Wednesday and Plymouth Argyle – were winning.
And, when it became clear that Eustace’s Blackburn were also ahead at champions Leicester, the celebratory mood began to evaporate.
By the end it had all gone very quiet, except for the 2,000 travelling Norwich fans who taunted their hosts with a chant of “Que sera sera, whatever will be will be, you’re going to Shrewsbury”.
At the end a small section of the home fans invaded the pitch.
As for Norwich, whose defeat dropped them to sixth, they now face a two-leg play-off semi-final with third-placed Leeds United.