By SABC Sport
7th March 2024
But it was not quite the perfect warm-up for Sunday's title clash with Manchester City after another injury blow.
The Uruguay international finished the last-16 first-leg tie with another on the stroke of half-time but it was his first in the 25th minute which was massively important - and not just because of the landmark it brought up.
Liverpool had been under a sustained spell of pressure after Alexis Mac Allister, taking over penalty duties from Nunez after his failure against Chelsea in January, had put them ahead.
Perhaps spurred on by that snub Nunez - out of nowhere, as is often his inclination - cut in from the left to whip a brilliant 25-yard dipping shot over goalkeeper Peter Vindahl.
His second effectively came when Mac Allister, head and shoulders above everyone else in possession, played a superb ball over the top which his fellow South American lashed across Vindahl and inside the far post.
Luis Diaz scored the fourth and Klopp even had the luxury of giving much-needed minutes to midfielder Dominik Szoboszlai - who scored the fifth - and forward Mohamed Salah on his return to tune them up for the weekend, but the loss of centre-back Ibrahima Konate to injury is another unwanted headache.
The gulf in class in terms of finishing was evident as Sparta, unbeaten at home all season, squandered a number of chances which could have made this much trickier whereas Liverpool were clinical and had plenty in reserve.
When the two sides last met in 2011 Kenny Dalglish's side played with a back five - which included such luminaries as Danny Wilson and Sotiros Kyrgiakos - with David Ngog leading the line.
The 2024 upgrade was quite considerable even though Klopp made three changes from the last-gasp win at Nottingham Forest with Jarell Quansah, Wataru Endo and Nunez coming in and put Salah on the bench after recovering from a muscle injury which had restricted him to one 46-minute substitute appearance since he suffered an injury at the Africa Cup of Nations mid-January.
It took them just six minutes to score as defender Asger Sorensen was a fraction late with his attempt to win the ball as Mac Allister charged out of midfield on the press.
With Salah absent, the Argentina international converted his ninth spot-kick in 10 attempts for English clubs, having previously scored eight for Brighton.
Sparta's response was immediate and sustained with Lukas Haraslin placing his shot too close to Caoimhin Kelleher with only the keeper to beat but it still needed Joe Gomez to acrobatically clear off the line.
Konate blocked Angelo Preciado's shot and then Kelleher tipped over when the Ecuadorian's header was helped on - but just when the pressure was reaching a peak Liverpool broke the shackles and Nunez doubled their advantage in true maverick style.
However, Sparta's bold approach in keeping three players high at all times succeeded in causing problems.
Jan Kuchta flicked over before Kelleher parried his shot into the path of Velijko Birmancevic six yards out but his finish was more suited to the circus pitched up across the road from the stadium as he bundled wide of an open goal after kicking the ball against his standing foot.
Cody Gakpo had two chances in quick succession to make the game safe but his shot on the turn was well saved by Vindahl and then he fired straight at the keeper from Diaz's delightful through ball.
Conor Bradley's first involvement after replacing Gomez at half-time in a pre-arranged swap was to divert Birmancevic's cross into his own net seconds after the restart and the unmarked Haraslin was crowded out by Kelleher.
The chaotic start to the second half continued when Konate was injured and replaced by Virgil van Dijk, with Szoboszlai coming on for Nunez.
Diaz's deflected 53rd-minute toepoke eventually put the game to bed before Salah had a goal ruled by VAR and Szoboszlai scored with the last kick of the game - however, Manchester City will not be so accommodating at Anfield.