Liverpool survived a 1-0 defeat in Naples in the group stage last season to go on and win their sixth European Cup, and this time a 2-0 reverse at the San Paolo made them the first reigning champions to lose their opening game in the competition since 1994.
Both sides had chances but the Group E clash was edging towards a goalless conclusion until a late penalty award for the hosts. Barely 10 minutes remained when Jose Callejon went down under an Andy Robertson challenge and German referee Felix Brych pointed to the spot.
Dries Mertens beat Adrian from 12 yards and substitute Fernando Llorente -- who played for Tottenham Hotspur against Liverpool in last season's final -- then took advantage of a rare defensive lapse by Virgil van Dijk to make it 2-0 in stoppage time.
Hat-trick hero Haaland
Liverpool must now bounce back in two weeks when they host Austrian champions Salzburg, who made a stunning return to the group stage as teenage forward Erling Braut Haaland netted a hat-trick in a 6-2 demolition of Genk.
Salzburg had fallen in the qualifying rounds in each of the last seven campaigns but finally progressed this season to the group stage for the first time since 1994-95.
Haaland, the teenage English-born Norwegian striker whose father Alf-Inge played for Manchester City, gave Salzburg a second-minute lead and netted twice more before half-time.
Aged just 19 years and 58 days, Haaland is the third-youngest player to score a Champions League hat-trick behind Wayne Rooney and Raul, according to sports statisticians Opta.
The South Korean Hwang hee-Chan and Dominik Szoboszlai also scored before the break for Salzburg, while captain Andreas Ulmer completed the rout in the second half.
Jhon Lucumi and Tanzanian striker Mbwana Samatta were on target for the Belgian champions.
Last season's Europa League winners Chelsea ensured it was two defeats out of two on the night for English sides as they went down 1-0 at home to Valencia.
The Spaniards scored in the 74th minute when a Dani Parejo free-kick was converted by Rodrigo Moreno. Chelsea were then given a chance to rescue a draw when Daniel Wass was penalised for handball in the box, but Ross Barkley's 87th-minute penalty hit the bar on its way over.
Also in Group H, last season's semi-finalists Ajax claimed an impressive 3-0 home win over Lille with two of their newest signings among the goals.
Quincy Promes headed the Dutch champions in front and the Mexican Edson Alvarez doubled their lead early in the second half before Nicolas Tagliafico sealed the win.
After a patchy start to the season, Barcelona will be relieved to escape from their trip to Borussia Dortmund with a 0-0 draw as Lionel Messi returned from injury as a second-half substitute.
The home side will feel they should have won, but Marco Reus had a second-half penalty saved before Julian Brandt hit the bar late on.
Those two appear well placed already to progress from Group F after Inter Milan needed a stoppage-time Nicolo Barella goal to rescue a 1-1 draw against rank outsiders Slavia Prague earlier.
Nigerian forward Peter Olayinka put Slavia ahead in the 63rd minute, only for Barella to level in the second minute of stoppage time after a Stefano Sensi free-kick hit the bar.
In Group G, RB Leipzig won 2-1 at Benfica with Timo Werner bagging a brace before Haris Seferovic pulled one back for the hosts.
Earlier, Memphis Depay's penalty gave Lyon a 1-1 draw at home to Zenit Saint-Petersburg after Iranian striker Sardar Azmoun had opened the scoring.
Wednesday's standout matches include Paris Saint-Germain against Real Madrid and Atletico Madrid against Juventus.