An early penalty from Alexis Mac Allister and a brace from Darwin Nunez helped Liverpool beat Sparta Prague 5-1 in the first leg of their Europa League round of 16 tie on Thursday.
Liverpool, who qualified for the knockout rounds as first in the group, dominated the match and went into halftime with a 3-0 lead to get closer to the quarterfinals.
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After Mac Allister was brought down inside the area, the Argentine gave Liverpool the lead from the penalty spot in the sixth minute. He sent Sparta goalkeeper Peter Jensen the wrong way when he fired into the bottom corner.
Núñez doubled the lead from distance in the 25th, slotting his shot just under the bar to score the 1,000th goal of Juergen Klopp's tenure.
The Uruguayan striker then made it 3-0 in first-half stoppage time after receiving a lofted pass from Mac Allister to score from the edge of the area.
Liverpool substitute Conor Bradley scored an own goal just after the break, but the visitors regained their three-goal lead in the 53rd minute thanks to Luis Diaz.
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Substitute Mohamed Salah thought he had extended Liverpool's lead to 5-1, but his goal was disallowed by VAR for offside.
However, Dominik Szoboszlai added a fifth in stoppage time.
In the other kick-off, AS Roma claimed a 4-0 victory over Brighton & Hove Albion. Paulo Dybala opened the scoring in the 12th minute and Romelu Lukaku doubled the lead before the break after a one-on-one with goalkeeper Jason Steele.
Defender Gianluca Mancini made it 3-0 for the hosts in the 64th minute before midfielder Bryan Cristante completed the rout four minutes later with a header.
Bundesliga runaway leaders Bayer Leverkusen overcame a two-goal deficit to rescue a 2-2 draw at Azerbaijan's Qarabag with goals from Florian Wirtz and Patrik Schick.
Sporting Lisbon and Atalanta drew 1-1 on Wednesday with striker Gianluca Scamacca scoring before half-time to cancel out Paulinho's first goal for the Portuguese hosts.
The match took place a day before Thursday's Europa League schedule, as UEFA safety rules do not allow teams from the same city to organize matches on the same day. Benfica will face Rangers in Lisbon in a later kick-off.
The return matches will be played on March 14.
