The visitors stunned Anfield in the 17th minute when Marcos Llorente finished a swift Atlético attack to put Diego Simeone’s side ahead. Julián Alvarez provided the assist as Liverpool were forced to respond after a difficult opening spell.
Liverpool gradually grew into the contest and found their equaliser shortly before half-time. Dominik Szoboszlai levelled in the 40th minute following a clever attacking move involving Ronald Araújo, sending the teams into the interval level at 1–1.
The Reds completed the turnaround just five minutes after the restart. Alexis Mac Allister produced a superb finish from outside the penalty area in the 50th minute, firing Liverpool into a 2–1 lead.
Atlético attempted to find a way back into the match, but Liverpool's defence held firm during the closing stages. The visitors introduced new signing Jonathan David as they searched for an equaliser, while Liverpool managed the game effectively to secure three points.
• Liverpool: Dominik Szoboszlai 40', Alexis Mac Allister 50'
• Atlético Madrid: Marcos Llorente 17'
The victory gives new Liverpool head coach Andoni Iraola a winning start in his first Champions League match in charge of the club. It also provides the Reds with an important three points at the beginning of the league phase.
Liverpool's summer signing Bradley Barcola made his first Champions League start for the club but was forced off in the second half with what appeared to be a calf injury.
Liverpool will now return their attention to the Premier League, with Fulham due at Anfield on Saturday, before their next Champions League assignment away to LASK in October.