Leeds United reaction: Thomas Christiansen insists Whites deserved more from Fulham draw
Fulham dominated large parts of the first half but Chris Wood, the Championship's top goalscorer in 2016/17, saw the best chance saved by David Button on a one-on-one.
Sone Aluko and Neeskens Kebano were denied in similar situations in the second period and Leeds had their moments in a thrilling finale.
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Hide AdThe teams could not be separated, though, as United were forced to settle for back-to-back 0-0 draws in front of their own fans.
"It's another clean sheet and I believe the team played a very good game," said Christiansen.
"We have to recognise that we played against one of the best teams in this league. They started very well and we were not fast enough.
"At the end of the first half we controlled the game a bit more and in the second we deserved more.
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Hide Ad"We need to be a bit more dangerous up front but at the end I'm satisfied with that result."
The previous four meetings between the sides had produced 1-1 draws, including last season's corresponding fixture in August when Wood's injury-time overhead kick rescued a point for Leeds.
The prolific striker continues to be linked with a move away from Elland Road but the most pressing issue for United with kick-off approaching was their lack of options at the back.
Leeds went into the campaign with only three recognised centre-backs and were forced to pair young midfielder Conor Shaughnessy with Pontus Jansson in the absence of Matthew Pennington and Liam Cooper.
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Hide AdTom Cairney was a notable absentee for Fulham, a player who had netted in each of his last four appearances against the club that let him go as a 16-year-old.
The visitors were also without the suspended Tomas Kalas and suffered an early scare when fellow defender Tim Ream received lengthy treatment on a facial injury.
The American returned to the field in time to see Stefan Johansen fire a 20-yard drive wide.Aboubakar Kamara saw an effort deflect behind before Ibrahima Cisse struck the base of the post as the slick away side continued to dominate.
Spanish playmakers Pablo Hernandez and Samuel Saiz lifted the home crowd and they were on their feet when Wood raced clean through from Ezgjan Alioski's well-weighted ball, only for Button to comfortably save his attempted chip.
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Hide AdFulham lost Lucas Piazon to injury and were then rescued by the offside flag as Wood volleyed home after taking Saiz's cross down on his chest.
The second half had threatened to burst into life but was still simmering when Kemar Roofe came on to replace Alioski just after the hour mark.
Hernandez wasted a good opportunity from a free-kick in a central position and Fulham captain Aluko dragged a shot wide as both sides pushed for a winner.
Kebano had a penalty appeal waved away by referee Darren Bond before Saiz shot wide at the end of a Leeds counter-attack.
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Hide AdThe game had become stretched with Fulham the next side to miss an opportunity, a golden one as Aluko was denied by Felix Wiedwald after being played in by Johansen.
Fulham played all but the opening minute of their weekend game at Reading with 10 men but there was no sign of fatigue as they went toe to toe with Leeds in the closing stages.
Only a last-ditch Shaughnessy tackle prevented Kebano from getting a shot in on goal after he was sent clean through while, at the other end, Kalvin Phillips scuffed an effort wide and a Stuart Dallas cross only narrowly evaded Wood in an eventful finish.