Premier League - Rodriguez hat-trick in Reds romp
Argentine Rodriguez added to the hat-trick he scored against Birmingham two weeks ago with another three against the Cottagers, taking his tally to seven in his last three games.
Dirk Kuyt and Luis Suarez also got their names on the scoresheet as Liverpool's upturn in form under Kenny Dalglish continued, with victory seeing the Reds climb two points above Spurs, who have a game in hand - against Manchester City - on Tuesday.
Moussa Dembele and Steve Sidwell were on target for Fulham, but the former's strike came too late at 3-0 down and the latter's was a mere consolation as time ran out. Defeat for the Cottagers, their first at home in eight games, sees them remain in 10th.
Liverpool, whose claim to be the most successful English side in domestic football was left hanging by a thread after Manchester United's win over Chelsea a day earlier, roared out of the blocks and effectively put the game to bed with barely a quarter of an hour played.
With £35 million striker Andy Carroll left on Merseyside, Kuyt and Suarez continued their partnership up front and, with Rodriguez posing a threat from the left and all three players on the top of their games, Liverpool simply blew Fulham away in a blistering opening to the game.
Javier Hernandez had claimed the fastest goal of the season at Old Trafford on Sunday, but Rodriguez wasted no time in eclipsing the Mexican's record, netting the opener with just 31 seconds on the clock.
Suarez was the architect, breaking free before playing a measured pass across the face of goal. The cross was deflected and Mark Schwarzer could only slide a clearance to Rodriguez, who buried the ball into the back of net to get the evening's scoring under way.
Rodriguez's second came in the seventh minute, the Argentine expertly volleying back past Schwarzer as he latched onto Glen Johnson's excellent deep cross to the back post.
Fulham were in total disarray and they were lucky to escape a penalty shout on 15 minutes when the labouring Brede Hangeland - back in the side having missed the weekend's win at Sunderland, but looking distinctly off the pace - appeared to push Suarez, who was bearing down on goal.
Referee Lee Mason waved play on, but Liverpool did not have to wait much longer for their third, this time the breakthrough arriving courtesy of an uncharacteristic goalkeeping howler by Schwarzer.
Kuyt's shot on goal appeared speculative at best, but Schwarzer allowed the effort to slip through his fingers and into the back of the net at his near post to gift Liverpool a three-goal lead after just 16 minutes of play.
From there on in, there was no way back for Fulham, although to their credit they fought bravely in the second half, introducing Bobby Zamora introduced from the substitute's bench.
Zamora headed on target, Clint Demspey fired over the bar and Eidur Gudjohnsen dragged a shot wide as the hosts gave their visitors something to think about.
And their improved play was rewarded when Zamora, with his back to goal, laid the ball off for Dembele to fire past Jose Reina and give Fulham some slight hope of getting back into the game.
Those hopes were short-lived though as Rodriguez completed his hat-trick in fine style, lashing the ball into the top corner on 70 minutes to open up a three-goal lead again and deflate whatever wind had gathered in Fulham's sails.
Five minutes later and Liverpool grabbed a fifth, Jonjo Shelvey slipping a pass through for Suarez to run on to, round the keeper and slot home with aplomb to register a well-deserved goal.
Sidwell matched Rodriguez's third with a thumping strike with four minutes remaining, but it was too little too late from Fulham and served as scant consolation as Liverpool ran out comfortable, and deserved, winners.