The Cottagers were far too good for their Yorkshire opponents and produced some slick football that would have graced the Premiership, and it will surely happen if they continue to play in this manner.
The game started with a bizarre incident, as Barnsley's recent signing from Real Oviedo, Mateo Corbo, was booked for throwing the ball away after less than a minute.
Corbo's aberration gave The Cottagers some vital momentum and they opened the scoring from a set piece deep in the Barnsley half.
Fulham's loan star Fabrice Fernandes whipped in a vicious left footed free-kick that found Saha and he powered a header past Kevin Miller from six-yards.
Almost immediately, the home side nearly doubled their lead when Carl Regan sliced a Fernandes corner against his own post, but it cannoned to safety.
Despite conceding the majority of possession, Barnsley were not without chances and Mike Sheron had a goal disallowed for offside, when it appeared that the forward was level.
Moments later, Sheron again had an opportunity, but he blazed over the bar when well placed, 10-yards out.
Sheron's miss appeared to break the concentration of the visiting defence, as they succumbed to a basic long ball goal.
Cottagers keeper Maik Taylor launched the ball up-field, Barry Hayles raced clear but his shot was well saved by Miller, only to see Saha ram the follow up through the legs of Chris Morgan and into the net.
Tykes boss Dave Bassett was planning his half time team talk, when Saha grabbed his hat-trick with the last kick of the first period.
Clever build up play released Bjarne Goldbaek and he was sent tumbling to the floor by Miller, and Saha confidently fired home the penalty.
The second half continued in the same vein, and the exciting Fernandes was unlucky not to get his name on the scoresheet, when his rasping 25-yard drive rattled the post.
A fourth goal eventually followed, Hayles converted a superb Saha cross from close range.
Shortly after the hour, the game descended into farce, when Mitch Ward received his second caution of the game, but was not dismissed after the referee had apparently forgotten the first yellow card.
Two minutes elapsed before the fourth official alerted referee Andy Hall to his error and Ward was given his marching orders, much to the delight of the Craven Cottage faithful.
This bizarre event appeared to break Fulham's concentration, as Matt Appleby broke clear to claim a consolation to take back to Yorkshire.
Fulham were stung into action once again, and Luis Boa Morte added a fifth late in the game.
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