It was supposed to be the night that Liverpool stretched their lead at the top of the table with Owen writing himself into the club's record books.
But impressive Fulham had not read the script. And in midfielder Steed Malbranque they had the best player on the pitch.
They produced a display of endeavour and excellent technique to more than deserve their point.
Liverpool, however, twice hit the woodwork and Owen ran himself into the ground in search of his goal.
The England striker had a hatful of chances but found Edwin van der Sar in top form and ended the night goalless.
Liverpool could not handle the fact that Fulham were prepared to go for them with pace and skill. That was not in the script either.
Emile Heskey returned to Liverpool side to partner Owen and Steven Gerrard came in for Jari Litmanen.
The Cottagers, seven unbeaten in the league, brought in Sean Davis for Sylvain Legwinski from the team that beat Everton at the weekend.
And with the confidence that has been building at Craven Cottage as their impressive start to life in the top flight, the West Londoners made Liverpool struggle from the off.
Quick movement, short, and sharp interplay made Liverpool work really hard to get their own game together.
Davies and Malbranque found time and space in midfield to bring Barry Hayles and Louis Saha frequently into the game, and Liverpool found themselves being hounded in their own backyard.
Liverpool's man of the moment Owen had one looping header saved by van der Sar, and saw a string of first-half chances slip from his grasp.
Fulham had their moments too, and only a superb tackle in the box by Gerrard on 19 minutes halted Luis Boa Morte in full flow after he had cut out a Sami Hyypia pass.
Saha then worked his way dangerously across the box looking for a shooting angle, and even though he scuffed his effort, the ball fell to John Collins, who forced Jerzy Dudek into a smart, low save.
Fulham were not doing the expected - sitting back and defending in depth - like the majority of visitors to Anfield. They worked hard to deny Liverpool time and space and constructed their moves, and produced plenty of enterprise of their own.
Owen almost scored though on 28 minutes when he took a pass from Danny Murphy and turned seven yards out to fire his shot far too close to van der Sar.
The Dutchman then made a point-blank stop from Owen, who had turned cleverly into space. The ball bounced up and onto the roof of the net.
Liverpool's best early chance though fell to Gerrard, who sent a header onto a post following a Gary McAllister free kick.
Liverpool were beginning to up their game and Owen turned Alain Goma and cruised into the box to fire in a shot that Steve Finnan deflected wide. The tide seemed to be turning Liverpool's way.
Soon after the break Owen then turned provider when he escaped down the right to fire over a low cross that Heskey somehow contrived to miss completely in the six yard box.
Then Liverpool hit the woodwork again when a long-distance McAllister free-kick from wide on the left struck the post.
Owen continued his one man battle with van der Sar by planting a header straight at the Fulham keeper, who was soon to frustrate Murphy too with a fine tip over following Berger's cross.
But it was the defending of Goma and Andy Melville, plus the running power of Saha, Hayles and Boa Morte than in the end gave Fulham their deserved share of the spoils.