Although two late goals added respectability to the scoreline, Leeds supporters were not fooled by this result and thousands headed for the exit long before the end.
But Wise, whose close relationship with chairman Ken Bates makes the sack extreme
ly unlikely, was unmoved, telling the punters that it is better aimed in his direction than at the players.
"Bring it on. Have a go at me. It is seriously not a problem," he said. "If they are going to have a go at someone, then have a go at me, don't put my players under more pressure.
"I understand that they're disappointed. They have got to be disappointed with the position we're in. But it's better that the fans have a go at me. I'm the manager of the football club and that is it. Leave the players alone. Me and Gus (Poyet) will take it. No problem."
The patience that Leeds fans have shown with the former Chelsea star snapped after 55 minutes when the Owls, who had been reduced to 10 men by the dismissal of Marcus Tudgay, went 3-0 up.
Various songs with anti-Chelsea messages rained down from the Don Revie Stand and there was an outburst of "Wisey, time to go!"
A season that sank to new depths on the eve of the game with captain Kevin Nicholls asking for a move had reached its lowest ebb. The players finally trooped dejectedly off, the sound of Snow Patrol's "The Final Straw" booming out of the tannoy system. However, when the results from other games involving teams in the relegation scrap came through, things suddenly began to look up.
Only Southend in the bottom six had gained a point so there was no change in the pecking order, just one game less to achieve safety. Where there is life, there is hope.
From Sheffield Wednesday's point of view, the game had been one of the highlights of a season destined to end with the intended goal of mid-table consolidation.
After a brief wobble, which saw the Owls taking just one point from seven games, things are back on course.
The Owls had hit Leeds with an early sucker punch when Tudgay sent a free header looping over goalkeeper Graham Stack and into the far corner of the net.
For a time it looked as if Leeds had frozen, their defenders hitting clearances straight at the opposition and midfield men acting like strangers.
Things briefly came together and, with different luck, they might have turned things around or at least got back on level terms before the break.
Ian Moore got round the back of the defence but goalkeeper Iain Turner made the first of a string of good saves and pushed the ball wide.
Leeds striker David Healy got nothing from referee Lee Probert, who ignored a penalty shout after a trip by Steve Watson and then looked away when Richard Wood pulled the striker back in a race towards the area.
Other referees might have red carded the Owls defender, who was highly impressive on his first start after a 13-month injury lay-off.
Owls defender Frank Simek had to produce a stunning goalline header to block a scissor-kick from Rui Marques as Leeds pressed but then came the turning point.
There should have been no danger when Frazer Richardson collected a pass from Stack on the flank but the Leeds defender stumbled into a challenge with Chris Brunt and lost the ball.
Brunt spotted Stack off his line and floated a stunning 35-yard shot into the net.
The chants from the Wednesday end ranged from "Two-nil, in your Cup final," to "Championship, you're having a laugh".
When Owls striker Tudgay picked up a second yellow card for unsporting behaviour, just four minutes after the restart, it could have offered a way back into the game for Leeds.
Not so. As Leeds pushed forward, they left gaping holes and Jermaine Johnson drilled in a third for Wednesday. Cue the vitriol.
Wednesday's defence held firm until the final three minutes when Lee Bullen sliced an attempted clearance into his own net and then Leeds striker Richard Cresswell scored.
Had it not been tor a tip over by Turner to deny Moore, Leeds might even have stolen a point.
This was the first time Leeds fans had seriously turned on Wise but if he should go on to save the club from relegation, an apology will be in order.
Leeds United: Stack; Richardson, Marques, Heath, Lewis; Howson (Blake 45), Kishishev (Carole 83), Douglas, Moore; Cresswell, Healy. Unused substitutes: Ankergren, J Johnson, Foxe.
Sheffield Wednesday: Turner; Simek, Bullen, Wood, Spurr; Jermaine Johnson (Small 72), Watson, Whelan, Brunt; Tudgay, Burton (MacLean 85). Unused substitutes: Adamson, Gilbert, Folly.
Referee: L W Probert (Gloucestershire).
MATCH FOCUS
HERO
Iain Turner: Owls goalkeeper produced a string of class saves.
VILLAIN
Kevin Nicholls: The Leeds captain who turned his back on his club.
KEY MOMENT
37th minute: Owls winger Chris Brunt disposesses Leeds defender Frazer Richardson and beats Graham Stack from 35 yards.
REF WATCH
Lee Probert: Showing red card to Tudgay was nearly as big a joke as his failure to show one to Richard Wood.
ENTERTAINMENT
Plenty of talking points although many Leeds supporters went home before the late drama unfolded. 8/10
VERDICT
Another abject display by Leeds, who only got back into the game at the end courtesy of generosity by a back-to-their-best Owls side.
WHO'S NEXT?
Leeds United v Luton Town, Saturday, March 10, Championship.
Sheffield Wednesday v Plymouth, Tuesday, March 6, Championship.
