The Reds join Manchester City, Arsenal and Brighton as the only sides with maximum points from two games of the new Premier League season.
Tougher tests lie ahead of Slot in his daunting task of succeeding Jurgen Klopp, starting with a visit to Manchester United next weekend.
But the early signs are positive for the Dutchman as his side are yet to concede and showcased their wealth of attacking options, spearheaded by Salah.
"Most players are quite used to what we want because it is not too different to what Jurgen did in the past," said Slot after building on an opening weekend win at Ipswich.
"We still have to prove a lot against teams that can end up in the top six."
Slot is expected to instill a more possession-focused approach than the one adopted by Klopp in his near nine years in charge.
However, Liverpool's opener was straight out of the Klopp copybook.
From a Brentford corner, Salah released Diogo Jota, who timed his pass perfectly into Diaz to charge through on goal and fire into the top corner on 13 minutes.
Thereafter there were only flashes of the football Slot is hoping to bring in the first half.
Brentford were again missing Ivan Toney, who is expected to leave the club before Friday's transfer deadline.
But the Bees still posed a threat without the England striker and should have levelled 10 minutes into the second half.
Nathan Collins met Mathias Jensen's enticing cross with a bullet header that Alisson Becker did brilliantly to parry.
That warning awoke Liverpool from their slumber early in the second period.
Collins made a goal-saving block moments later to deny Jota turning in Trent Alexander-Arnold's low cross.
Vitaly Janelt was next to get a vital foot in to prevent Salah rounding off a slick team move.
Brentford goalkeeper Mark Flekken then produced a brilliant stop to turn Diaz's powerful effort behind.
As is so often the case, the Reds had to turn to Salah to provide the clinical finish to finally make the points safe.
The impressive Diaz this time bagged the assist and the Egyptian managed to time his run perfectly to remain onside and dink the ball over Flekken.
"In the first half there is more energy in the other team, then in the second half it eventually leads to gaps that open up," added Slot.
"In the end Brentford didn't have the legs anymore to defend us."
Slot was serenaded in the closing stages by the 60,000 crowd chanting his name -- as they had been instructed to do by Klopp at his farewell in May.
For much of last season Liverpool looked on course to give Klopp a glorious goodbye as they rivalled City and Arsenal for the title until falling away in the final weeks of the season.
There has been much consternation among the Liverpool support at the lack of a single new signing heading into the final week of the transfer window to strengthen that squad.
But they look best placed of the rest to push City and Arsenal again if there is to be a three-way battle for the title.
