beat Ajax Amsterdam 1-0 away with a fortunate own goal in their UEFA Champions League group stage opener on Wednesday.
They rode their luck at times but still showed their title credentials.
Ajax full-back Nicolas Tagliafico turned the ball into his own net in the 35th minute to ensure a winning start in Group D for the English champions.
Liverpool looked the stronger of the two teams in spite of Ajax creating several good chances at the Johan Cruyff Arena.
Davy Klaassen struck the post with a powerful shot and Quincy Promes had a point-blank effort stopped by the legs of Liverpool goalkeeper Adrian.
This went on as the Dutch club created a handful of excellent opportunities.
Yet Liverpool, who won their sixth UEFA Champions League title in 2019, still proved value for their victory.
They dominated possession and counter-attacked at pace while keeping a clean sheet in spite of missing defensive talisman Virgil van Dijk, who suffered a serious knee injury at the weekend.
Fabinho moved from midfield to central defence to replace Van Dijk and had an outstanding game, notably hooking a clearance off the line to deny Dusan Tadic just before half-time.
It was one of several chances for Ajax in the first half.
Lisandro Martinez had a header saved by Adrian and Ryan Gravenberch shot narrowly wide, much to the annoyance of Liverpool manager Juergen Klopp.
Klopp spent the early part of the game berating and shouting instructions to his players.
But his agitation was quelled when Sadio Mane turned the Ajax defence with a swift body movement to set up the goal.
He miskicked his own effort, but it caught Tagliafico as he clumsily tried to clear and instead deflected it into the Ajax net.
“It was a good enough performance to win the game, which at moments was pretty wild.
“It was not one of our sunny shiny world class football days. It was not perfect but the boys fought like crazy,” said a more satisfied Liverpool manager afterwards.
Klopp took off Mane and his strike partners Roberto Firmino and Mohamed Salah with 30 minutes still left.
But replacements Diogo Jota and Takumi Minamino kept up the pressure on the home team.
Ajax should have equalised, however, four minutes into stoppage time when Adrian did not properly deal with a cross into the area.
But substitute Jurgen Ekkelenkamp missed the target.
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