Messi was on target as Paris Saint-Germain came from behind to win 3-1 at Maccabi Haifa to make it two victories from two games.
Tjaronn Chery hinted at an upset by giving the hosts the lead after 24 minutes.
But Messi equalised before the break, scoring against a 39th different opponent in the competition – another record.
Benfica also have two wins in Group H following a 2-1 victory at Juventus.
Arkadiusz Milik put Juventus ahead after four minutes, but Joao Mario levelled from the penalty spot and David Neres scored Benfica’s winner.
Reigning champions Real Madrid left it late to beat RB Leipzig 2-0 at the Bernabeu.
Los Blancos were forced to wait until the 80th minute to break the deadlock, Federico Valverde curling home a left-footed shot.
Substitute Marco Asensio sealed the points in stoppage time with an immaculate finish from Toni Kroos’ cutback.
The other Group F game saw Celtic draw 1-1 draw with Shakhtar Donetsk in Poland.
The Ukrainian side, who have been displaced from their home stadium since 2014, attracted close to 30,000 at Legia Warsaw’s stadium.
Celtic took a 10th-minute lead when Rio Hatate’s effort deflected off the sliding Artem Bondarenko, but Mykhaylo Mudryk equalised against the run of play near the half-hour mark.
AC Milan top Group E after beating Dinamo Zagreb 3-1 at the San Siro.
Olivier Giroud, from the penalty spot, Alexis Saelemaekers and Tommaso Pobega were on target for Milan, with Mislav Orsic replying for Dinamo.
In the same section, Graham Potter’s first game as Chelsea manager ended in a 1-1 draw with RB Salzburg at Stamford Bridge.
Raheem Sterling’s superb curler just after the interval was cancelled out by Noah Okafor 15 minutes from time.
England midfielder Jude Bellingham headed Dortmund in front after 56 minutes, but John Stones and Haaland struck in the final 10 minutes.
Copenhagen and Sevilla fought out a goalless draw in the other Group G game, giving City a three-point lead in the section after two games.
Ten-man Rangers suffered a 3-0 defeat to Napoli at Ibrox, where penalties proved the turning point of the game.
Allan McGregor saved a retaken Piotr Zielinksi spot-kick on the hour after Gers defender James Sands was sent off conceding it.
But McGregor was beaten from 12 yards in the 67th minute by Matteo Politano.
Substitutes Giacomo Raspadori and Tanguy Ndombele wrapped up Napoli’s win.