Former Sheffield Wednesday youngster Morrison, who had been on loan at Valley Parade, signed a two-year deal last week, and tormented the home side all afternoon.
Morrison's most telling contribution won the match for City in the 42nd minute. He expertly controlled Nicky Summerbee's throughball and turned past Town defender Nat Clarke before firing home.
Bradford were rampant in the last 15 minutes of the first half and should have been at last three up by the break.
Dean Windass hit the left hand upright after 38 minutes with a curling free-kick and Mark Bower hit the bar from a Summerbee corner in stoppage time.
The impressive spell was sparked by Town midfielder Jon Worthington's foul on Steven Schumacher that should have resulted in a straight red card.
Worthington had been hacked and kicked all game by David Wetherall and Lee Crooks without getting any protection from referee Phil Joslin and finally exploded back in a fit of rage.
Worthington's two-footed lunge on Schumacher should have been more harshly punished than with just a yellow card, but it served to fire up Bradford to take the game by the scruff of the neck.
Huddersfield boss Peter Jackson changed his side's formation from 3-5-2 to 4-4-2 for the start of the second period by bringing on winger Danny Schofield for defender David Mirfin - and the switch had the desired effect.
Town looked a more dangerous proposition with Schofield pulling the strings and were unlucky not to level when both Chris Brandon and Pawel Abbott hit the woodwork.
Brandon also forced Bantams keeper Paul Henderson into a fine diving save on 83 minutes after he took on Abbot's terrific pass down on the left edge of the box.