Liverpool recorded their 3rd consecutive win, and clean sheet, in a dominant display away at Arsenal in the Premier League.
With Chelsea having fallen to their first defeat under new manager Thomas Tuchel earlier in the day, it gave the reds a glimpse at mounting an unlikely charge back into the top four.
The reds have been beset with woe since the turn of the year, but the return of Fabinho into midfield couple with growing trust in youthful defensive pair Ozan Kabak and Nat Phillips has given fans hope for an improvement in fortunes in the final weeks of the season.
Roberto Firmino was preferred in the starting line up to Diogo Jota, mostly due to conditioning following the international break, but it was Jota's arrival that eventually turned Liverpool's dominance in possession into an adequate scoreline.
Trent Alexander-Arnold also showed his continuing return to fine form - it was his perfect cross that led to Liverpool's opening goal in the middle of the second half.
Diogo Jota's two goals took his tally to six from just the last four games. He is right up there in terms of players settling quickly at a new football club.
Mohammed Salah was also on target. A 26th goal of the season as he heads towards another 30+ goal season. 120 Liverpool goals in less than 200 appearances.
Liverpool's gap to 4th placed Chelsea is now just two points, but both Spurs and West Ham still have to complete their weekend fixtures which could see the reds pushed down to 7th place.
Klopp acknowledged that the reds still have work to do and it is out of their hands, but they have taken a tentative step forward to ensuring they are back in the Champions League next season.
"It was a very important statement. In our position it is clear, everything that has happened to us this season means we don't have it in our hands.
"We have to win our games and others have to lose but we have to put pressure on them. That is what we did with the result but we are still not in. We have to fight and we will fight and that is the statement for us and nobody else."
The reds can taken other steps forward when they face Real Madrid in the first leg of the Champions League quarter final on Tuesday.