The Reds had won just four of their first 11 games of the season and fell behind for the eighth time this campaign when Scott Arfield fired the Glasgow giants into an early lead.
But Rangers are being schooled on their return to the Champions League for the first time in 12 years as they crumbled to a record-equalling European defeat in the second half.
The Glasgow giants remain without a point and have conceded 16 goals in four games.
"The first half and the last half an hour was night and day," said Van Bronckhorst. "I cannot explain it.
"The performance was not the way we want to represent this club."
Roberto Firmino's double either side of half-time turned the game around before the Brazilian teed up Darwin Nunez to kill off the contest.
Klopp had left Salah, Thiago Alcantara and Diogo Jota on the bench with one eye on Sunday's clash against Manchester City in the Premier League.
But they were brought on in the final quarter and Salah did not miss the chance to cash in against a beleaguered Rangers defence.
The Egyptian's treble arrived in just six minutes and 12 seconds to beat the previous record held by Bafetimbi Gomis in Lyon's 7-1 win over Dinamo Zagreb in 2011.
"It changes the mood definitely, and that's good," said Klopp. "We all know who is coming on Sunday. That will be different, but it's better to go in with the feeling from tonight.
"When we play to our potential we're a pretty good football team. That's what we showed tonight."
Harvey Elliott rounded off the scoring on a sobering night for a Rangers side that only months ago reached the Europa League final.
A draw in Amsterdam will suffice for Liverpool to reach the last 16 when they face Ajax in two weeks' time.
But Napoli remain out in front in Group A after a 4-2 win over Ajax sealed their place in the knockout stages.
FAMILIAR SLOW START
Klopp's team selection was partly a reaction to losing Trent Alexander-Arnold, Joel Matip and Luis Diaz to injury in a 3-2 defeat by Arsenal on Sunday that left the Reds already 14 points adrift of the Premier League leaders.
The visitors have made a habit of slow starts this season and were caught cold again when Arfield's run was not tracked from midfield and the former Canadian international produced a brilliant finish to find the bottom corner.
Fortunately for last season's Champions League finalists, Rangers' own defensive frailties were exposed for the equaliser on 24 minutes.
Not for the first time this season, Giovanni van Bronckhorst's men were guilty of soft defending from a set-piece as Firmino was given the simple task of nodding in Kostas Tsimikas' corner.
Liverpool clicked through the gears after the break with Firmino again doing no harm to his case to be handed a contract beyond the end of this season.
Firmino stroked home his eighth of the season from Joe Gomez's fine low cross and then teed up Nunez as the Uruguayan grabbed another much-needed goal for his fragile confidence by curling into the far corner past Allan McGregor.
Rangers' 40-year-old goalkeeper performed heroics to keep the score down as Liverpool won the first meeting between the sides 2-0 at Anfield last week.
But McGregor's age showed as Salah came off the bench to end his goal drought from open play in style.
Salah fired in from a narrow angle before catching out McGregor on his near post and then completed his hat-trick with a sumptuous finish on his left foot.
The pain was not over there for Rangers as Elliott swept home the rebound after McGregor denied Jota and a VAR review overturned the linesman's initial decision to rule the goal out for offside.
