Left-back David Murphy bagged a first-half brace, the second of which a super free-kick, to put the hosts firmly in control at half-time.
Tom Adeyemi added a well-taken third after the break before on-loan Manchester United striker Jesse Lingard got in on the act late on, making amends for an early penalty which he saw saved by David Forde.
It was Birmingham's third emphatic victory in succession on home soil following a 4-1 Sky Bet Championship triumph over Sheffield Wednesday and a 3-1 Capital One Cup success against Swansea.
And that brings particular joy for Clark, whose Blues side only managed seven wins from 23 league outings at home last term and suffered humiliating 5-0 and 4-0 defeats to Barnsley and Watford respectively along the way.
"I was absolutely delighted," Clark said.
"What has really pleased me is that I've been desperate to deliver performances for the home fans and I think in the last three home games we've delivered performances of the highest level.
"We've scored 11 goals and could really even have scored more.
"What's pleased me as well is the clean sheet.
"I'm an attack-minded manager and I love my teams to entertain but I just feel we've got so many matchwinners at the top end of the field that if we can keep more clean sheets this season, we've got lads who can produce a bit of magic."
Murphy, 27, was making only his third appearance since returning from almost a year on the sidelines following knee surgery.
And Clark has welcomed him back with open arms.
"I've said all along I believe David's the best left-back outside the Premier League," he said. "He seems to be enjoying his football.
"The first goal he's taken with aplomb and the second one is a fantastic finish."
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