Ajax should have taken a third-minute lead but Steven Berghuis struck a gilt-edged opportunity against the right post, with the midfielder curling narrowly wide shortly after.
A resolute Liverpool continued with their backs against the wall before Andy Robertson smashed a rare Reds chance just off target, but Klopp’s visitors soon hit the front.
LiveScore reports that Jordan Henderson delicately chipped through for Salah to neatly lift over the onrushing Remko Pasveer, before Nunez inexplicably smashed the left post with the goal gaping two minutes later.
Nunez made amends after the interval, heading Robertson’s corner in off the right post before Elliott fired into the roof of the net two minutes later.
Substitute Kenneth Taylor blasted a presentable opportunity over after the hour mark, though Ajax never threatened an unlikely comeback.
Underwhelming returns in the Premier League thus far have led to scrutiny for Liverpool, though the Reds emphatically delivered in what was their 150th match in the Champions League.
Klopp will take encouragement from the Reds’ fourth straight victory in the competition over Ajax – only Real Madrid (seven) have managed a longer such streak – leaving Alfred Schreuder with much to ponder.
Ajax, whose first-half dominance failed to pay dividends, will likely settle for a Europa League place after falling to a seventh loss in nine home games against English sides in Europe.
Super Salah
Salah may be yet to hit his usual heights in the Premier League, but the forward collected his 42nd goal in the Champions League – only Didier Drogba (44) has more among African players.
The Egypt international presented a constant threat on the right flank, scoring in a fourth straight game in the competition for just the second time, as well as assisting Elliott for the third goal.
Bad from Berghuis
Berghuis was left to rue his two early missed chances, the first of those a routine finish that the midfielder would have been expected to slot past Alisson and into the back of the net, LiveScore reports.
Those errant efforts summarised a frustrating outing for Ajax, who started in dominant fashion but faded away rapidly after Salah’s first-half opener.
What’s next?
Liverpool host Premier League strugglers Leeds United on Sunday, while Ajax are not in action until their final Champions League game at Rangers on Tuesday.