Jermaine Beckford netted a first half winner as fourth-bottom City were booed off the pitch as the home faithful watched back-to-back league defeats at St Andrew's for the first time since March 2011 - coming after the abject 5-0 rout by Barnsley, the club's biggest home league defeat in 25 years.
Reports of a player revolt were dismissed this week but Clark, who insisted pre-match he held no grudges against the club who sacked him in February, watched a disappointing display here, shaky in defence and short of bite in attack, particularly in the first half.
Huddersfield were good value for their half-time lead, with Beckford's
first goal since joining on loan from Leicester putting his side ahead.
Nathan Redmond, Blues' brightest spark, crashed a curling effort against a post in the first half, but Blues' task was made even harder by the 74th-minute dismissal of substitute Nikola Zigic for a high challenge on Callum Woods.
Clark applauded both sets of supporters prior to kick-off but he almost saw his new club fall behind inside the opening minute.
Beckford turned Curtis Davies, who later hobbled off, far too easily and fed James Vaughan, whose spin and shot from 10 yards went wide.
Town certainly started on the front foot and Peter Clarke headed over from a corner before both Redmond and City debutant James Hurst soon went close at the other end.
Davies came to Blues' rescue after 17 minutes with a superb sliding challenge to nick the ball off the toes of the shooting Keith Southern.
Birmingham's defending was at sixes and sevens and they finally got punished after 25 minutes.
Adam Clayton found Vaughan in acres of space down the right and he crossed for Beckford, who eased ahead of Steven Caldwell, to sweep home from close range.
Blues were in need of inspiration and Redmond tried to do just that with sweet curling effort against the inside of the far post from 20 yards.
But Huddersfield were looking strong and long-range efforts from Danny Ward and Oliver Norwood both brought good saves from Jack Butland before the interval, which was greeted with boos from the home faithful.
Zigic was brought on by Clark at the interval to add a different dimension to Blues and it worked.
Chris Burke saw a 55th-minute effort tipped over by Alex Smithies before curling just wide from the resulting corner.
Clayton blasted wide from Norwood's corner while Clarke, despite being pulled up for a foul, headed against the crossbar.
Blues were rightly reduced to 10 men with 16 minutes remaining when Zigic was shown a straight red card for a high challenge on Woods.
Butland denied Beckford with a great save before Wade Elliott somehow headed straight at Smithies in injury time with the goal at his mercy.
It was enough to see Town, in the first league meeting between the two sides since 2001, secure their first three points against Birmingham since 1996.