Yossi Benayoun was the star of the show for Liverpool, scoring three times for Benitez's men and setting up the fourth for Dirk Kuyt, as the Clarets were swept aside 4-0 on Merseyside.
Liverpool's ability to challenge Manchester United and Chelsea for the title has been questioned in the opening weeks of the season, with defeats against Aston Villa and Tottenham Hotspur derailing their charge.
Those losses had even prompted Anfield goalkeeper Jose Reina to call into question his own side's capabilities, but there were few problems on their latest outing.
After staging a last-gasp comeback against Bolton ahead of the international break to reignite their season, Benitez's men were back in business at Anfield, steamrollering Owen Coyle's Burnley.
Visiting goalkeeper Brian Jensen was by far the busier of the two keepers and it seemed a mater of when and not if Liverpool would race into an early lead.
The game was effectively done and dusted at the break as Benayoun and Kuyt scored before half-time, while a double from the Israeli in the second 45 minutes wrapped up the points.
Benayoun got the ball rolling just before the half-hour mark, cutting inside Graham Alexander to slide in a shot across goalkeeper Jensen for the all-important opener.
Four minutes before the half-time interval it was 2-0, as Jensen could only parry Benayoun's shot at the end of a swift counter-attack and Kuyt slotted in the loose ball to extend the Reds' lead.
Benayoun then tapped in Steven Gerrard and Andriy Voronin passes to round off an impressive display, completing his hat-trick eight minutes from time.
Two Martin Paterson long-range strikes were Burnley's only threat but they were comfortably gathered by Reina as Liverpool rarely looked in trouble.