The £1.3million record signing from Bradford was behind two goals in three minutes midway through the first half to send Town on their way on a comfortable afternoon.
Wells fired the ball across the face of the box from a free-kick on 29 minutes for Keith Southern to prod home from close range and moments later Danny Ward profited from the Bermuda international's good work.
After the break Huddersfield ran riot with Wells at the heart of all they did as Adam Hammill, Adam Clayton and Sean Scannell got on the scoresheet.
Barnsley, who have won just once away all season, had shown little sign of the wide-margin defeat to come when they started strongly. The visitors could have been two goals up before Town scored but for good defending.
Nick Proschwitz was twice denied, first by Anthony Gerrard's block and then by goalkeeper Alex Smithies at his near post.
The Tykes at that stage were well in the game, but the match turned on an incident involving former Town full-back Jack Hunt.
Hunt, on loan at Oakwell after the Terriers sold him for £2million to Crystal Palace in August, brought down Hammill on the left edge of the box on 29 minutes.
Clayton's free-kick bobbled in the box and fell eventually for Wells, who fired across the face of the box for Southern to tap in for his first goal of the season. It was also the first time the ex-Blackpool enforcer has scored for Town at home.
Ward then swept home when Wells created another opportunity to send Town into half-time 2-0 ahead.
After that Barnsley were rarely in it and could have lost by more, with Wells in inspired form.
He was unlucky not to score on 44 minutes with an audacious lob after Steele and a defender got in a muddle on the edge of the box.
A minute earlier Hunt had Barnsley's best chance when he struck a 20-yard curler just over the bar from Jacob Mellis' pass.
Wells put Hammill clear on 48 minutes and the winger bundled in the rebound after Tykes keeper Luke Steele parried his first effort.
Wells capped a fine performance by winning a penalty on 58 minutes, converted by Clayton. Ex-Leeds midfielder Clayton put Wells through and he was brought down by Steele as he tried to round him in the box.
Clayton, who took the ball off Wells, struck a confident spot-kick past Steele high into the top-left corner. Wells wanted to take the penalty as he has not scored in seven matches - his worst run since a 10-match streak at the Bantams last season.
Frontman Wells was at it again on 70 minutes when he set Ward up for a 20-yard curler which Steele parried. Substitute Scannell completed the 5-0 rout four minutes from the end.