Charlie's Adam injury-time strike was little consolation for Blackpool but Irvine has breathed new life into Wednesday and their new-found resolve was evident throughout at a bitterly cold Bloomfield Road.
Eyebrows were raised when Irvine, 51, was shown the door at Preston earlier this month but he wasted no time in getting back into work and has rapidly stamped his mark on the underachieving Owls.
The former Everton assistant boss began with a 2-1 victory at Barnsley on Saturday - Wednesday's first win in three months - and this latest success was well deserved.
The result prevented Blackpool from climbing into the top six but should pour confidence into Irvine's team as they brace themselves for the tests that lie ahead.
A biting, swirling wind was hardly conducive to freeflowing football but Blackpool should have led inside the ninth minute when Daniel Nardiello flashed a header just wide.
Jermaine Johnson, Wednesday's matchwinner at Oakwell, was the visitors' most lively player in the opening quarter.
The Jamaican's pace was too much for Blackpool in the 18th minute as he outstripped centre-back Ian Evatt and delivered a teasing low cross from the right.
Marcus Tudgay strode forward to strike a low right-footed shot wide of Paul Rachubka's far post when he should have at least hit the target.
Yet two minutes later Blackpool went desperately close to breaking the deadlock when Adam swung in a vicious free-kick and Evatt thumped a close-range header against a post.
In the 24th minute, Johnson succumbed to what appeared to be a hamstring strain and was replaced by Clarke.
Eight minutes into the second half, it was Wednesday's turn to hit the woodwork as Tudgay showed neat control to chest the ball down and strike a left-footed shot against the post from 12 yards.
Wednesday were not to be denied and they opened the scoring in the 71st minute when Soares collected possession 20 yards from goal and drove a right-footed shot into the top corner.
Blackpool should have then equalised but substitute Gary Taylor-Fletcher fired straight at Owls goalkeeper Lee Grant and Wednesday made the points safe with six minutes remaining.
Darren Potter swung in a free-kick from the left and Clarke rose highest to head the ball past a stranded Rachubka, before Adam drove home his goal from 25 yards shortly before the final whistle.