Dudek drops Reds in it
The Polish goalkeeper's horrendous howler on 64 minutes provided the platform for The Red Devils' victory and a rapid-fire second from Forlan gave his side the decisive advantage.
Sami Hyypia grabbed a late goal which set up a grandstand finish but a combination of stubborn defending and Fabien Barthez's heroics ended United's barren streak against their fierce rivals.
It was an engrossing encounter from the first whistle with both sides striving to play open, expansive football.
Liverpool roared out of the blocks and Milan Baros's stinging 25-yard rocket produced a strong stop from Fabien Barthez with barely a minute on the clock.
United hit back as Ryan Giggs's curling free-kick was glanced on by Ruud van Nistelrooy but straight at Dudek.
Michael Owen then tried his luck from distance while at the opposite end Ole Gunnar Solskjaer had a goal chalked off after he was fractionally offside following neat interplay between van Nistelrooy and Forlan.
It was helter-skelter stuff with Liverpool controlling possession but unable to probe in behind the visiting defence and allow Owen to stretch his legs to decisive effect.
Midway through the half, Jamie Carragher made a timely intervention to deny Solskjaer a shooting chance after van Nistelrooy had robbed Hyypia.
Gary Neville was also in the right place on two occasions, charging down Djimi Traore's shot and then nicking the ball off Owen's toes at the back post.
The frenetic pace of the game barely eased up throughout the opening period and Solskjaer forced a sprawling save from Dudek with a low 25-yard effort.
The closest Liverpool came to a goal in the first half was Vladimir Smicer's devilish curler which arced just the wrong side of the upright.
After the break, the match resumed in a similar vein but clear-cut chances were scarce, although Forlan hesitated, rather than pulling the trigger, after being fed by Giggs.
Reds boss Gerard Houllier shuffled his pack approaching the hour mark, throwing on Emile Heskey for Baros.
On 64 minutes, The Red Devils capitalised on almighty howler from Dudek, who must now surely be fearing for his place as Liverpool's first choice keeper.
Barthez's long punt forward was headed back to Dudek by Carragher but the Pole inexplicably let the ball slip through his grasp and Forlan was on hand to roll the ball over the line.
Three minutes later and the Uruguayan was on target again after excellent work from Paul Scholes and Giggs, provided Forlan with a clear sight at goal and his rasping drive scorched past Dudek into the back of the net.
In chasing the game, Liverpool introduced El Hadji Diouf for the largely ineffective Smicer and applied the pressure on the United rearguard with Owen spinning sharply in the box and shooting straight at Barthez.
Forlan tried to turn provider as United sought to wrap the game up but van Nistelrooy's control uncharacteristically deserted him.
With less than ten minutes remaining Reds captain Hyypia handed his side a lifeline, rifling the ball into the bottom corner after a scramble in the box.
The Finn's goal injected renewed vigour into Liverpool's approach and Dietmar Hamann's thunderous drive was magnificently pushed away by Barthez.
In injury-time, the largely anonymous Steven Gerrard dragged a shot wide and Wes Brown hacked away as Liverpool grappled for an equaliser but the visitors were not to be denied a priceless three points.