In a game of few clear chances, the striker climbed highest at the back post to beat his former Bradford team-mate Jon McLaughlin with a powerful header from close range.
It brought to an end a four-match winless run on the road for David Wagner's side while inflicting only a second home defeat in nine outings for Burton.
The result was harsh on Nigel Clough's men who had the lion's share of the chances in a fast-flowing and often entertaining encounter but could not quite find their way past a stubborn and resilient Terriers back line.
Jamie Ward had the best Burton chances of the night but his namesake Danny in the Huddersfield goal was equal to anything
Albion edged what was a high-paced first half that was lacking in real goalmouth action.
The better chances fell to Burton with Jamie Ward the only man in yellow to test Huddersfield's on-loan Liverpool goalkeeper.
He cut inside midway through the half after neat approach play but put his shot straight at the stopper.
Huddersfield looked pacy on the break but were unable to get Wells into scoring positions, midfielder Philip Billing mustering the Terriers' only real effort of the first 45 minutes with a low drive that was comfortable for McLaughlin in the Burton goal.
Ward fired a free-kick over in the early second-half exchanges with Elias Kachunga going close for Huddersfield with a drilled effort that Damien McCrory had to block almost on the goal line.
Albion's best chances continued to fall to Ward, the clearest chance coming to the on-loan Forest forward midway through the second half as he scuffed a shot into the ground from Jackson Irvine's deep cross.
A spate of yellow cards late on threatened to ruin the game, none more so than the one for Michael Hefele when referee Jeremy Simpson pulled back play with substitute Will Miller clean through on goal.
Moments later Wells made his decisive intervention, heading beyond McLaughlin.
Kachunga was denied a second goal for the visitors late on by an excellent challenge from the returning Kyle McFadzean.
The result was good enough to keep Wagner's men in fourth in the Championship table and well in the hunt for the play-offs while Albion slip to 21st but still crucially two points off the relegation places.
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