The Terriers should have taken the lead in the 12th minute when Jacob Butterfield released the run of Grant Holt through the middle, but the striker lost his composure and poked the ball past the post.
Wells should have equalised for Chris Powell's side when he beat the offside trap and ran through on goal.
The striker saw his initial effort saved by Dean Gerken, and then somehow fired the rebound over the bar from close range.
Ipswich started the second half well and nearly doubled their lead as David McGoldrick raided down the right and crossed into the middle, but Conor Sammon could not get the touch needed for a certain goal.
Mick McCarthy's side did double their advantage when Christophe Berra latched onto McGoldrick's cutback in the box and calmly placed the ball past Smithies from close range, after the visitors failed to clear their lines from a corner.
The Terriers should have got themselves back in the game when Paul Dixon raided down the flank and hit a good cross into the box, but Holt could only guide his headed attempt over the bar.
Huddersfield were handed a chance to get back into the game as Luke Chambers pushed Holt over in the area and a penalty was awarded. Wells took the spot kick and fired the ball past Gerken.
Powell's side nearly equalised when Holt headed the ball into the path of Harry Bunn at the back post, but Gerken made an excellent save to deny the winger.
The Terriers completed their comeback when Wells notched his second goal of the game by latching onto Sean Scannell's cross at the back post to power a header past Gerken.
Wells could have won the game for Huddersfield late on when played through on goal by Bunn, but he blasted his shot over the bar, as both sides settled for a point in an entertaining Championship clash.