The Aussie was hauled off after 64 minutes, to a chorus of boos from the Leeds away support, following another woeful display and the big man's Elland Road career looks all but over.
Viduka who had a training ground bust-up with Reid earlier this week, looked uninterested from the start as Reid's Premiership stars crashed to defeat from goals in each half from Burgess and Allsopp to follow their 4-2 defeat by Burnley last Sunday.
Nigel Martyn played what could be his last game for the club. The former England keeper is expected to join Chelsea next week. The only bright spots for Reid were the returns of Dominic Matteo and Michael Bridges.
UNITED 0 HULL 2
(At the KC Stadium, Attendance 17,216, h/t 0-1)
(Thanks to the Hull City AFC website for providing the following match details);
A bumper crowd of 17,216 turned out to see Burgess put Hull in the lead after 14 minutes and then Allsopp put the game beyond United with a second half wonder strike that had Nigel Martyn clutching at thin air.
City had the first attack of the game, after a shot produced the first corner of the game in the 2nd minute.
A Stuart Green corner was floated into the Leeds penalty area but Stuart Elliott could only direct his header well wide.
After some good tracking back by Damien Delaney on the left, City broke with Danny Allsopp collecting the Irishman's long ball.
Allsopp turned and tried to cross the ball out wide but Ian Harte blocked the ball before it could reach Jason Price out on the right.
The referee was first called upon after a rash challenge by Jason Wilcox left Alton Thelwell on the floor.
Wilcox received a stern talking to from the man in black but was not issued with a yellow card much to the dismay of the home crowd.
City were now gaining in confidence and it showed when the Tigers took the lead after 15 minutes.
Danny Allsopp held the ball up well in the middle of the pitch and played the ball to Jason Price on the right hand side.
Price then produced a perfect delivery towards Ben Burgess who planted his header past the diving Nigel Martyn.
It was only what City deserved after seeing the best part of the game so far.
Leeds then introduced their first substitute of the game with only 17 minutes gone in the game.
Promising youngster James Milner replaced Jason Wilcox after another challenge by the midfielder left Richard Hinds in a heap.
With confidence now sky high, City went in search of another goal.
Some good skills by Jason Price led the ball being played through to Stuart Green.
Green took the ball in his stride and took the ball past the Leeds defence but shot straight into the arms of Nigel Martyn in the Leeds goal.
The Premiership side then produced their first chance of the game with 23 minutes gone.
James Milner slotted the ball through to leave Alan Smith one on one with Alan Fettis.
Smith poked the ball past Fettis but the Leeds striker saw his effort ruled out with the linesman's flag up for offside.
Peter Reid's side began to look a little more composed going forward and started to have more play in the Tigers defensive third but the City defence was equal to the task.
With 34 minutes gone on the clock, a mistake by Alton Thelwell gifted the ball to Alan Smith.
Smith passed the ball out wide to James Milner whose cross was just to high for a climbing Mark Viduka and the danger was over.
Leeds broke again with a Dominic Matteo long ball finding Alan Smith running through.
Smith collected the ball but with the use of a hand according the referee's assistant, a decision that the Leeds forward clearly disagreed with.
Leeds kept pressing and were almost gifted a goal when a Jason Price back pass played Alan Fettis in trouble.
Fettis went to clear the ball but his clearance was blocked by James Milner and went for a goal kick.
That ended the first half action and as the referee's whistle went a huge roar came from the City fans to show their appreciation of a good first half display from Peter Taylor's men.
The Tigers kicked off the second half and straight away carried on with the good form they showed in the first half.
Danny Allsopp struck the ball from 20 yards out but his shot was always rising and caused Nigel Martyn no problems.
City were almost through again in the 51st minute when Allsopp was played through by Burgess but the Australian was pulled down in the Leeds box which went seemingly unnoticed by the referee.
Stronger claims for a penalty came from the City players just a minute later.
Jason Price was running through and after a pull of his shirt from a Leeds defender went down but City didn't get anything from the referee again.
Peter Taylor made his first change of the game after 58 minutes.
Having received a knock on a previous challenge, Ian Ashbee was brought off with Dean Keates replacing the central midfielder.
Leeds then made some changes of their own on the hour mark.
Peter Reid brought on Stephen McPhail and Danny Mills to replace David Batty and Ian Harte.
The changes couldn't stop City attacking once more though.
Again, Danny Allsopp hit a tremendous shot from the edge of the penalty area and it was in all the way until the right hand of Nigel Martyn steered the ball over.
Leeds then introduced fans favourite Michael Bridges after 64 minutes replacing Australian striker Mark Viduka, who left the field with the sound of boos from the Leeds fans.
City then made another change with Richie Appleby replacing Stuart Green after 69 minutes.
Leeds came forward and won a corner but the resulting cross was easily cleared by Richard Hinds.
The ball fell at the feet of Stuart Elliott who raced away into the Leeds half but was fouled by Danny Mills on the left hand side.
The ball was crossed in from the free kick but went over the heads of all the players and out for a Leeds throw in.
City won the ball straight back though and after some neat passing play from Price and Thelwell, the ball fell to Dean Keates.
Keates placed a superb ball to the far post and the incoming Stuart Elliott dived to meet the ball but it seemed to just behind Elliott and the Leeds defence cleared their lines.
Elliott came straight back though and unleashed a cracking half volley that seemed in all the way but somehow went wide.
With 78 minutes gone on the clock, City extended their lead with a cracking goal.
Danny Allsopp collected the ball 20 yards out and unleashed an unstoppable drive past Nigel Martyn to delight the home crowd.
It was a case of third time lucky for Allsopp after seeing two previous long-range efforts prove unsuccessful.
City boss Peter Taylor then took off his strike partnership after 80 minutes.
Burgess and Allsopp came off to a great applause to be replaced by young strikers Danny Webb and Clayton Donaldson.
The Tigers were now playing some great passing football and showed the Premiership side how it was done.
With three minutes to go, City attacked again with Stuart Elliott hurtling down the left flank.
The Northern Ireland winger was determined and strong with only a last ditch tackle from Danny Mills prevented Elliott from testing Nigel Martyn.
Hull City: Alan Fettis, Richard Hinds, Marc Joseph, Alton Thelwell, Damien Delaney, Ian Ashbee (Dean Keates 58mins), Stuart Green (Richie Appleby 69mins), Stuart Elliott, Jason Price, Ben Burgess (Danny Webb 80mins), Danny Allsopp (Clayton Donaldson 80mins).
Subs: Justin Whittle, Richie Appelby, Steve Burton, Clayton Donaldson, Russell Fry, Dean Keates, Steve Melton, Paul Musselwhite, Carl Regan, Danny Webb.
Leeds United: Nigel Martyn, Gary Kelly, Ian Harte (Danny Mills 60mins), David Batty (Stephen McPhail 60 mins), Michael Duberry, Matthew Kilgallon, Nick Barmby, Dominic Matteo, Mark Viduka (Michael Bridges 64mins), Alan Smith, Jason Wilcox (James Milner 17mins).
Subs: Danny Mills, Scott Carson, Stephen McPhail, Frazer Richardson, Simon Johnson, Michael Bridges, James Milner.
Ref: P Joslin (York)