Liverpool may be about to be knocked off their perch by Manchester United, but they showed on Monday they might just mount a serious challenge for a 19th league title of their own next season by destroying Fulham at Craven Cottage.
The Reds made it 13 goals in their last three games and Maxi completed his second hat-trick over the same period, with Dirk Kuyt making it 12 goals in his last 13 matches for club and country and Luis Suarez wrapping up the rout.
The win moved Liverpool back above Tottenham into fifth and left Fulham stunned as they paid the price for a horrible first 16 minutes which saw them 3-0 down.
The Cottagers threatened a comeback when Moussa Dembele pulled a goal back but they were 5-1 down before Steve Sidwell fired a late consolation.
If Jamie Carragher was worried his 666th appearance for Liverpool - moving him second on the all-time list - was a bad omen, he was in for a pleasant surprise.
It was Fulham who must have thought they were cursed as they endured calamity after calamity right from kick-off.
The first blunder came from Aaron Hughes, whose slip let in Suarez, with Carlos Salcido and Mark Schwarzer making a hash of the striker's left-wing cross and allowing Maxi to thread the ball home.
The shocking defending continued in the seventh minute as Chris Baird played Glen Johnson onside and the full-back crossed for Maxi to volley in from close range at the far post.
Liverpool were rampant, to the glee of the large travelling contingent, and Suarez saw a penalty appeal turned down before a absolute howler from Schwarzer made it 3-0.
There was little power in Kuyt's shot from just inside the penalty area but the goalkeeper allowed the ball to squirm underneath him at the near post, all but killing the game as a contest.
Suarez wasted a glorious chance to pull the ball back for Raul Meireles to make it 4-0 and Maxi volleyed over the top as Fulham's defending in wide areas continued to be non-existent.
Fulham - whose only threat had been a Dembele air shot - finally got going and Dempsey saw his half-volley from Simon Davies' corner cleared off the line by Johnson.
Home boss Mark Hughes threw on Bobby Zamora for Davies at the break and Liverpool suffered a blow when Raul Meireles appeared to pull a hamstring and was replaced by Jonjo Shelvey.
That came after a Fulham free-kick, which Zamora flicked on dangerously moments before Dempsey fired just over the crossbar.
Eidur Gudjohnsen also dragged wide as the home side created more in five minutes than they had in the opening 45.
And they deservedly pulled a goal back in the 57th minute when Martin Skrtel gave Zamora the chance to lay the ball off to Dembele, who curled home beautifully beyond Jose Reina.
The keeper was furious, belting the ball into the stands and earning himself a yellow card.
Hughes would have been cursing himself for not starting with Zamora.
Liverpool remained a threat on the break, particularly through the outstanding Suarez.
But it was Maxi who killed off any hope of a Fulham fightback with 20 minutes remaining, completing his hat-trick with a stunning 25-yard drive into the top corner.
Suarez made it another five-star performance for Kenny Dalglish's men when he raced onto Shelvey's through-ball and brilliantly rounded Schwarzer to prod home the goal his performance deserved.
The Uruguayan beat the offside trap again moments later only to blaze over the top.
Dembele was replaced by Gael Kakuta before Maxi left the field to a standing ovation, with Joe Cole coming on.
Fulham kept going and, with just under five minutes left, Sidwell pounced on a loose clearance and cracked a lovely 20-yard half-volley into the top corner.
Schwarzer saved brilliantly from Shelvey, Spearing had a shot cleared off the line and Kuyt's point-blank shot was blocked by Baird in stoppage-time.