In the Dutchman's first competitive match in front of the Kop, Liverpool broke the Bees' resistance early doors through a Luis Diaz counter-attacking goal, but offensive inspiration was otherwise in short supply.
Thomas Frank's men - who showcased their own potent threat when given the chance to surge forward - often managed to snuff out Liverpool's passing moves and defend their box well, leading to a noticeably flat Anfield atmosphere.
Mark Flekken and Nathan Collins in particular earned their keep at the back for Brentford, but whatever choice words Slot had for his players at half time went down a treat, as the Reds began to carve out chances at will as the final quarter approached.
Such an attacking resurgence eventually paid off when Mohamed Salah broke a personal duck, scoring in the first two weeks of a Premier League season for the very first time to kill any faint Brentford hopes of a late fightback.
Indeed, the Egyptian's effort sucked the remaining life out of the Bees, who can be proud of aspects of their Anfield performance but were ultimately punished for failing to make the most of the opportunities that they were presented with.
Liverpool could have also shown more attacking intent in the first half in particular, but Slot's men demonstrated their counter-attacking excellence and ability to rapidly move up a gear in what was a merited victory.
LIVERPOOL VS. BRENTFORD HIGHLIGHTS
Luis Diaz goal vs. Brentford (13th min, Liverpool 1-0 Brentford)
The first Anfield Premier League goal of the Slot era arrives after just 13 minutes, as Liverpool turn defence into attack in the blink of an eye and strike first through Diaz.
The Reds deal with a Brentford corner, and Diogo Jota sprints forward to lead a two-on-two counter-attack. The Portuguese fires a crisp pass through to Diaz, who made a brilliant run across Bryan Mbeumo, and the Colombian fires a left-footed finish into the roof of the net.
Mohamed Salah goal vs. Brentford (70th min, Liverpool 2-0 Brentford)
A relentless period of Liverpool pressure finally pays off, as the Reds double their lead through Salah, who times his run to perfection, opens up his body and delicately guides the ball into the far corner.
However, that move was all about Dominik Szoboszlai, who showcased brilliant strength to hold off Fabio Carvalho and lay the ball off to Alexis Mac Allister, who subsequently lays off Diaz to go from scorer to provider.
MAN OF THE MATCH - LUIS DIAZ
Brentford duo Flekken and Collins - who put his body on the line for his side time and time again - certainly warrant honourable mentions, but Diaz was playing like a man possessed on Merseyside and was too hot for the Bees backline to handle.
As well as producing a clinical first-half finish, his run across Mbeumo to fashion the opportunity was perfectly timed, and he ended the afternoon with the assist for Salah's effort before being taken off.
Whether the frequent transfer speculation has played its part in Diaz's scintillating form only he knows, but the Colombia international could hardly be doing more to prove that his long-term future lies with Liverpool.
LIVERPOOL VS. BRENTFORD MATCH STATS
Possession: Liverpool 62%-38% Brentford
Shots: Liverpool 19-8 Brentford
Shots on target: Liverpool 8-2 Brentford
Corners: Liverpool 9-4 Brentford
Fouls: Liverpool 10-7 Brentford
BEST STATS
WHAT NEXT?
A reunion with bitter rivals awaits Liverpool in gameweek three, as the Reds head to Old Trafford to clash with Manchester United next Sunday afternoon.
Meanwhile, Brentford travel to Colchester United on Wednesday in the second round of the EFL Cup before hosting Southampton in the top flight next Saturday at 3pm.