Jurgen Klopp's side started the game well, then fizzled out before their perseverance paid off right before added time when the central defender headed to put his side in front.
This is Ajax's first defeat of the season, while Liverpool are back to winning ways after a tough start to the season both in the Premier League and Europe.
Liverpool are rewarded for their perseverance
Jurgen Klopp described Liverpool's 4-1 defeat at Napoli last week as the worst game of his seven-year tenure and the Reds responded with an improved display against Ajax, ultimately rewarded for their perseverance in a 2-1 win. Liverpool deserved the 17th-minute lead given to them by Mohamed Salah's 15th Champions League goal at Anfield -- surpassing Steven Gerrard's record -- and could easily have been further ahead by the time Ajax struck back.
Mohammed Kudus took his goal superbly against the run of play and Liverpool palpably lost confidence thereafter. Yet despite not being at their riproaring best, the home side kept plugging away and found the breakthrough a minute from time as Joel Matip headed home Kostas Tsimikas' corner. Klopp looked more relieved than ebullient at confirmation the ball had crossed the line. This is only Liverpool's fourth win from nine matches across all competitions but it will feel like a big step in the right direction.
Matip capitalises where Van Dijk couldn't
Liverpool ended this game with 23 shots but the highest individual number came from an unlikely source: Virgil van Dijk. Ajax's vulnerability from set-pieces -- or really any high ball into the box -- was obvious and the Liverpool centre-back never had a better chance than when left unmarked from Trent Alexander-Arnold's 35th-minute delivery.
He forced Remko Pasveer into a fine save and worked the Ajax goalkeeper again two minutes before the interval when meeting Tsimikas' delivery from the opposite side. Van Dijk had four efforts in all -- but it was Matip who came good -- after missing an earlier chance of his own -- beating Pasveer for his third Champions League goal and first since December 2013 for Schalke. It was also his first match-winning goal since joining Liverpool in 2016.
A sense of déjà vu about Liverpool's defensive weaknesses
The cancellation of last weekend's Premier League fixtures due to the passing of Queen Elizabeth II may have given Liverpool more time to work on their defending but the goal they conceded here had a distinct sense of déjà vu and a failure to learn from past mistakes. Not for the first time this season, Alexander-Arnold was found wanting. Steven Berghuis drifted in behind him to pull the ball back where Kudus was given time to turn and unleash a superb effort which crashed in off Alisson's crossbar.
The goal bore marked similarities to Jadon Sancho's opener when Manchester United beat Liverpool 2-1 last month; after another foray down Liverpool's right, the United winger received the ball in the box and had an age to find the net. Liverpool ultimately got themselves over the line but the pattern of vulnerability will not have gone unnoticed by their rivals. With no game now until October 1, Klopp will have plenty to time to ponder a better way to solve it.
Ajax: Pasveer 7, Rensch 7, Timber 7, Bassey 7, Blind 7, Alvarez 7, Taylor 7, Tadic 7, Berghuis 7, Bergwijn 6, Kudus 7.
Subs: Sanchez 6, Grillitsch 6, Brobbey 6.
Best and worst performers
BEST: Thiago. He used the ball intelligently and helped Liverpool maintain pressure on Ajax during their best spells in the game.
WORST: Elliott. The 19-year-old has been one of Liverpool's better performers this season but he struggled to make a meaningful impact here and was substituted as Liverpool chased a winner.
Highlights and notable moments
Mo Salah is now four goals away from being the highest scoring African player in the history of the Champions League.
The 22-year-old Ghanaian scored back to back goals for Ajax in the Champions League for the first time in his career.
Matip provided the late drama at Anfield.
After the match: What the managers, players said
"He doesn't hesitate, eh? He doesn't wait long. When he finds a date for that, he can call me. He forgets that in the big sports in America, these players have four-month breaks so they are quite happy they can do a little bit of sport in these breaks. It is completely different in football. What can I say? Imagine that: United players, Liverpool players, Everton players altogether in one team. It is not a national team. North against south. And all the London guys together, Arsenal, Tottenham, great. Did he really say it? Interesting." - Klopp on Chelsea owner Todd Boehly's suggestion of a Premier League North vs. South all-star game
Key Stats (provided by ESPN Stats & Information)
- Mohamed Salah ends a 7-game scoring drought in the Champions League, the longest of his career.
- Mohammed Kudus has scored 5 goals in his last 4 games for Ajax.
- Joel Matip's 3rd career UCL goal and first since 2013-14 with Schalke. This is his first game-winning goal since joining Liverpool.
Liverpool: Jurgen Klopp's side are off to a slow start in both the Premier League and Champions League this season, and have a tough set of matches ahead, despite their next game against Chelsea being postponed. The Reds will face Brighton at home on Oct. 1 in the Prem, followed by their next Champions League match against Rangers on Oct. 4, and then a visit to the Emirates on Oct. 9 to face Arsenal, who are top of the table.
Ajax: The Dutch side are off to a winning campaign in the Eredivisie and in Europe, with no shortage of goals. They'll face fourth place Alkmaar on Sept. 18, then struggling side Go Ahead Eagles on Oct. 1, followed by a home game against a fired up Napoli side in the Champions League