A late goal from Keith Andrews salvaged a much-deserved point for Albion.
The Seagulls were heading for their second defeat in three days, after a host of near misses, last ditch tackles and an injury to Leo Ulloa – on his first game back from a three-game suspension – had conspired to go against Oscar Garcia’s side.
But with just a minute left on the clock, Andrews met Stephen Ward’s cushioned header to cancel out Matty Fryatt’s first-half opener.
On the back of Saturday’s defeat to Ipswich, Albion showed real intent from the start and twice caught out a static Wednesday defence in quick succession.
David Lopez just failed to latch onto Bruno’s deft flick over the Owls’ rearguard, while Ulloa found himself clean through on goal but was denied by Chris Kirkland who was quick off his line to smother the ball.
Wednesday, with plenty of height in their side, looked a threat on the break but with their attacking forays restricted to the right flank, they were repelled by Ward who made a couple of fine challenges.
Albion, too, were using the right flank with success and they created another opening on 23 minutes when Inigo Calderon’s cut-back was met by Andrew Crofts, but the midfielder failed to get a good connection on the ball.
Crofts also tried his luck from distance with a daisy cutter, following a sweeping move involving Bruno and Kazenga LuaLua, while the livewire winger drove a free-kick wide of Kirkland’s upright.
Such was Albion’s dominance, Tomasz Kuszczak was brought into action for the first time on 35 minutes when he collected Reda Johnson’s header from a Lewis Buxton free-kick.
LuaLua had appeals for a penalty turned down two minutes later, as he went down under a challenge from Buxton, but the home crowd who were silenced three minutes before half-time.
Fryatt – making his first start for Wednesday on loan from Hull City – met Jeremy Helan’s centre and with his back to goal turned to fire past Kuszczak.
There was still time for Gordon Greer to send a header into the arms of Kirkland from a David corner and Albion would have been frustrated to go in at the break a goal behind.
Will Buckley replaced Calderon at half-time, with Bruno reverting to his more familiar right-back berth, but Albion’s evening soon went from bad to worse when Ulloa turned an ankle and was stretchered off.
He was replaced by Kemy Agustien, while Ashley Barnes entered the fray soon after, and the pair almost got Albion back on level terms on the hour mark.
The Dutchman did well to fire a ball into the feet of Barnes, but the striker’s first-time left-foot shot fell the wrong side of Kirkland’s post.
Buckley was then foiled by a last-ditch tackle from Miguel Llera, while Andrews also went agonisingly close with a volley following LuaLua’s fine run and cross.
But he would not be denied with just one minute left on the clock; a fine ball into the box by Crofts was met by Ward and his Irish compatriot was on hand to grab his first goal of the season.