The hosts deserved their win and ended a run of five games without conceding for the Black Country side, though the 49th-minute goal came thanks to a bizarre attempt to clear by Saturday's matchwinner Karl Henry which landed at the grateful boot of Ferenczi.
Andy Keogh's penalty followed almost immediately afterwards but the highly-rated German goalkeeper Muller was equal to it.
Wolves made the livelier start and Stephen Foster did well to block a Matt Jarvis shot as he cut in from the left.
Barnsley had the first clear opening after a quarter of an hour when Jamal Campbell-Ryce's powerful drive was well parried by Wayne Hennessey, diving low to his left.
Ferenczi then headed goalwards from another Werling cross but Hennessey saved comfortably on 26 minutes.
Barnsley seized control in the final 10 minutes of the half. Jamaica wide man Campbell-Ryce came close again when a Dominik Werling cross on 38 minutes made its way to the far side but his shot was deflected wide off Darren Ward.
Anderson de Silva then hit one straight down the throat of Hennessey before a Campbell-Ryce piledriver from long range flew just wide.
Werling was the main threat and his 25-yard free-kick was only kept out by a brilliant Hennessey save after 42 minutes.
The hosts started the second half as they ended the first and Foster's cross-cum-shot was blocked at the near post by Hennessey - and four minutes into the half they were ahead.
Martin Devaney crossed from the right and the chance looked to have gone but Henry's bizarre attempt to clear, a diving header, fell kindly for the Hungarian Ferenczi to tap in.
Two minutes later Wolves had a penalty after substitute Stephen Elliott, on for Jarvis, was fouled by Lewin Nyatanga but Keogh's spot-kick was parried by Muller.
The goal and the saved penalty appeared to inspire Barnsley, who started knocking the ball around well with the impressive Campbell-Ryce and captain Brian Howard to the fore.
Seyi Olofinjana dragged a right-foot shot wide of Muller's right-hand post midway through the second period as McCarthy brought on Freddy Eastwood.
Jon Macken had a chance to double the lead when Ferenczi slotted a pass to him but his first touch was poor and Hennessey came out to narrow the angle.
Eastwood twisted and turned to make a shooting position but his effort was weak, and Tykes substitute Sam Togwell pulled a left-foot shot well wide from 30 yards.
Midfielder Henry - the matchwinner in the weekend victory over Preston - tried to make amends for his earlier mistake but his right-foot effort went wide as the game entered its final 10 minutes.
Anderson's low shot was fielded by Hennessey but Ferenczi's effort proved enough for a merited home win.
Any reproduction, publication or redistribution of this material without the written agreement of 365 Media Group is strictly forbidden.