But while Fulham dominated possession, they created few clear-cut chances early on and West Brom continually threatened on the counter attack.
Liverpool, who are still chasing a Champions League spot, face Burnley at Turf Moor while Fulham take on Everton at Goodison Park.
Juventus appeared happy with their lead while Fulham, with an away goal in the bag, also seemed happy to shut up shop.
But it was the dismissal of Nevland that had changed the course of the game and, while Fulham had a measure of control beforehand, they were forced into a rearguard action after the dismissal.
Stoke joined Sunderland on 20 points from 14 matches after drawing 0-0 at Blackburn, while Fulham came from behind to earn a 1-1 draw at Bolton, who stayed in the bottom three.
Rafael Benitez's Liverpool side will take on Atletico Madrid after overcoming Benfica 4-1 at Anfield to win 5-3 on aggregate, while Fulham won 1-0 at German champions Wolfsburg for a 3-1 aggregate victory and will face Hamburg in their last-four encounter.
Elsewhere, Liverpool's disappointing start to the season continued as they were held goalless at Anfield by Stoke, while Southampton and Fulham drew 2-2.
In other action on the final day of the season, Arsenal clinched third spot with a 4-0 home win over Europa League finalists Fulham while north London rivals Tottenham Hotspur stay fourth after losing 4-2 at relegated Burnley.
But injured loanees Matt Saunders and Michael Uwezu have returned to Fulham, while Nathan Baker and Brian Gilmour picked up knocks against Burton.
Aston Villa remain in 16th place after 1-1 draw against Fulham, while mid-table West Ham United and Southampton also played out a 1-1 draw.
Andy Johnson had a header cleared off the line for Fulham, while Hull keeper Matt Duke saved from long range Paul Konchesky and Clint Dempsey strikes.
Former Manchester United striker Van Nistelrooy was foiled by Schwarzer after latching on to Dennis Aogo's pass and battling his way past a couple of Fulham defenders, while Piotr Trochowski twice shot wide from about 20 yards.
Arsenal finished third after a 3-2 win at West Brom to secure their Champions League place, while north London rivals Tottenham Hotspur beat Fulham 2-0 to take fourth.
In a fractious affair, Hull were hurrying and scurrying around Craven Cottage breaking up Fulham's play, while the home side had a calmer front as they tried to work an opening.
In his absence, Tottenham will rely on fellow strikers Peter Crouch, Roman Pavlyuchenko and Robbie Keane while England could turn to Crouch, Fulham's Bobby Zamora or Sunderland striker Darren Bent who scored the third goal in Tuesday's 3-1 qualifying victory in Switzerland.
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Lerner is a fellow American, while Bradley had previously been linked with the Fulham managerial position before the appointment of former Manchester City boss Mark Hughes.
Fulham midfielder Simon Davies saw three penalty appeals turned down by referee Phil Dowd while the loss of Zamora - who has broken his right leg just above the ankle - did not help Fulham's cause as they lost their way in the first half.
Davies' inclusion owes much to injuries to Tottenham striker Jermain Defore, Fulham's Bobby Zamora and Aston Villa forward Gabriel Agbonlahor while Capello has also overlooked Newcastle United's Andy Carroll who had been tipped for a call up.
Fulham substitute Eric Nevland later saw his shot turned around the post while Pizarro's cross was sent just wide by Riise at Schwarzer's far post.
Fulham had beaten Liverpool last Saturday and were a team high on confidence, while Roma showed the struggle for form their 14th place in Serie A indicated.
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