The second goal came midway through the first half as Kyle Lafferty curled a fine free kick over the wall and into the corner from 25 yards out.
Lafferty almost doubled his personal tally in the 38th minute when he latched on to Elliott Bennett's cross, but his looping header came back off the crossbar.
Norwich made eight changes at the break but still managed to pick up where they left off, with Ricky van Wolfswinkel taking advantage of a Hamann error to walk the ball into an empty net just two minutes after the restart.
It was 4-0 less than 10 minutes later as Nathan Redmond's long-range strike found the bottom corner, while Hamann was on hand to prevent another goal shortly afterwards as he denied Lewis Grabban.
It was merely delaying the inevitable, however, and the Canaries got their fifth just after the hour mark courtesy of a Johnson strike from the edge of the box.
Braintree did get themselves on the scoresheet with 20 minutes to play as Marks fired home from close range after the Norwich defence had failed to deal with a cross.
The five-goal lead was restored with just four minutes remaining, however, as Van Wolfswinkel capped off the scoring with his second of the night after being set up by Josh Murphy.