The Blackburn loanee headed in from Jay Tabb’s cross early in the second-half to give Blues a lifeline after goals from Nahki Wells and James Vaughan had put Huddersfield in control at the break.
Varney and Tommy Smith both went close to an equaliser but the Terriers held on to dent Blues’ promotion hopes.
Mick McCarthy made two changes to the side that drew with Bournemouth on Good Friday, with Chris Wood and Richard Chaplow in for Freddie Sears and Teddy Bishop as Blues kicked off defending a six match unbeaten run against Huddersfield.
Town were inches away from a goal inside the first two minutes, Tabb forcing the ball goalwards from Richard Chaplow’s cross but Mark Hudson and Alex Smithies combined to clear off the goalline.
Sean Scannell had a shot blocked, the Terriers’ midfielder then doing well at the other end to thwart a surging run from Cole Skuse.
It was the home side who edged ahead on 12 minutes, Wells, who scored twice when the teams met in the 2-2 draw at Portman Road in October, capitalised on a loose ball from
Zeki Fryers and curled a left footer past Bart Bialkowski from the edge of the box.
Smithies held firm from Daryl Murphy’s header, then Wells sidefooted wide after his strike partner Vaughan had set him up.
Town had an anxious look at referee Tony Harrington when Scannell went down under Fryers’ challenge inside the box, the official keeping his whistle silent.
Wells and Vaughan continued to cause problems for the Town defence, Bialkowski saving from Vaughan’s overhead kick eight yards out, then at the other end Murphy beat the offside trap and rounded Smithies but saw Terriers’ Tommy Smith clear off the line.
Huddersfield extended their lead just past the half hour, a terrific ball from Jacob Butterfield was met by an equally good header by Vaughan that nestled in the far corner of the net.
Oscar Gobern curled a left foot effort over the bar from 25 yards as Chris Powell’s side threatened a third, Town’s frustration illustrated by bookings for Christophe Berra and Tommy Smith for fouls before the break.
Bishop and Sears replaced Chaplow and Wood at the break as the Town boss changed things around and Blues were back in the game within three minutes of the restart, Tabb’s cross met by Varney’s header into the net.
Huddersfield responded, Wells denied at the nearpost, then from the following corner, Bialkowski produced a brilliant double save from close range.
Varney threatened an equaliser for Blues on the hour, taking Bishop’s pass in his stride, cutting inside but Smithies was in the right place to make the save.
Jonny Williams was introduced soon after for his first appearance since his return to the Club, Tabb making way.
Sears looked to get on the end of Luke Chambers’ cross but Hudson cleared, Bialkowski comfortably dealt with Butterfield’s effort at the other end as the game still hung in the balance.
Town’s Tommy Smith cleared for a corner as the dangerous Wells looked to get in, the striker then volleying over from the flagkick, Smith curling just wide of the Huddersfield goal moments later.
Blues threw men forward in search of an equaliser but it wouldn’t come, the defeat leaving Town just outside the top six with five games to play.
Huddersfield: Smithies, Smith, Hudson, Lynch, James, Coady, Butterfield, Gobern, Scannell (Wallace 90), Wells (Edgar 81), Vaughan (Lolley 90). Subs not used: Allinson, Holmes, Carroll, Majewski.
Town: Bialkowski, Chambers, Smith, Berra, Fryers, Skuse, Tabb (Williams 66), Chaplow (Bishop 46), Varney, Wood (Sears 46), Murphy. Subs not used: Gerken, Clarke, Anderson, S.Hunt. Booked: Berra, Smith.