In Irvine's first match in charge, the struggling Hillsborough outfit put one over their South Yorkshire rivals.
Wednesday got off to a dream start when they went ahead after just three minutes, stunning the home fans.
Two corners in quick succession had Barnsley in a mess and, with the second, Michael Gray curled in a dangerous ball that troubled keeper Luke Steele.
Steele punched the ball down and it dropped invitingly for Wednesday full-back Tommy Spurr who stabbed the ball over the line from close range.
The lead lasted just four minutes as the Tykes equalised with a hefty slice of good fortune. Iceland international midfielder Emil Hallfredsson linked smartly with Carl Dickinson on the left and swung in a dangerous looking deep cross.
Wednesday keeper Lee Grant - a possible target for former Wednesday manager Brian Laws at Burnley - was caught out and the ball dropped over him into the net.
Barnsley striker Daniel Bogdanovic might have done better with a swift break but Mark Beevers did enough to deal with the danger and, when the Malta striker broke again, he missed another opportunity.
Wednesday, brimming with confidence, were denied when Steele produced a fingertip save from James O'Connor's fierce effort.
The visitors were back in front after 21 minutes when Marcus Tudgay flicked the ball on after Barnsley had failed to clear their lines effectively. The flick sent in Jermaine Johnson and he rammed his shot past Steele.
Barnsley had a strong penalty appeal dismissed when Hallfredsson went down in the box and the Tykes were denied a second equaliser when Stephen Foster's header was headed off the line by Darren Potter.
Seconds before the break Steele produced another vital stop when Johnson burst forward and was poised to add another goal.
Wednesday almost added a third goal just seconds after the break when the impressive Johnson cashed in on a mistake by Foster but Steele produced an important save.
Barnsley boss Mark Robins made one desperate throw of the dice 25 minutes from the end with a triple substitution, bringing on winger Jamal Campbell-Ryce and strikers Andy Gray and Iain Hume but Wednesday hung on.