Ahmed Elmohamady, Robert Koren, George Boyd, Tom Huddlestone and Matty Fryatt were all on target as the Tigers ended 2013 on a high, with the Fulham firmly in the relegation zone.
Fulham went into the match looking to secure back-to-back away wins in the Premier League for only the second time since May 2011, but instead fell to its heaviest defeat in the top flight.
After a goalless first half, Hull ran riot after the break, Ahmed Elmohamady breaking the deadlock three minutes into the second period.
Robert Koren fired in the second on the hour mark, before George Boyd added the third just three minutes later as Fulham wilted.
Tom Huddlestone rounded off an impressive display by netting his first Premier League goal since April 2011 and second-half substitute Matty Fryatt added number five with 16 minutes left.
Koren knocked home a rebound in the closing stages after David Stockdale - who helped Hull to promotion on loan last season - spilled a Danny Graham effort in the six-yard box.
Hull manager Steve Bruce made three changes from the team which lost to Manchester United on Boxing Day, but the club's biggest boost was goalkeeper Allan McGregor’s inclusion, despite being forced off against United through injury.
Fulham had won at Norwich City two days previously but Rene Meulensteen named six alterations to that side, with Hugo Rodallega and Bryan Ruiz slotting back into the attack.
Hull steadily grew into the game and Fulham was saved only by the frame of the goal in the 19th minute as Huddlestone's curling free kick from the right almost snuck into the bottom corner, with Stockdale keeping Boyd’s close-range effort out soon after.
Fulham's attacking threat was virtually non-existent and Hull had the best of the chances, Elmohamady striking down Stockdale’s throat and Yannick Sagbo bending an effort wide.
The home side began the second period in determined fashion and after Huddlestone, Sagbo and Koren all went close, Elmohamady gave the club a 49th-minute lead as he prodded a half-volley into the roof of the net after Fulham failed to clear a corner.
Hull doubled the advantage 11 minutes later. Sagbo produced a perfectly-timed delivery into the area from deep and Koren arrived to knock past Stockdale.
Things got even worse for Meulensteen’s strugglers in the 63rd minute as Boyd hit a 20-yard left-footed shot into the bottom corner for his first top-flight strike and Huddlestone netted an almost-identical strike just a few moments later to celebrate his 27th birthday in fine style.
The magnificent Huddlestone was also instrumental in Hull’s fifth. His 35-yard free kick was tipped on to the crossbar by Stockdale, but substitute Matty Fryatt was on hand to grab his first Premier League goal.
Bruce's men were still not done. With just over five minutes remaining, Stockdale made a mess of a Graham shot and Koren pounced on the rebound to complete a resounding scoreline that leaves Fulham 18th in the Premier League with the division's worst goal difference.