Atletico Madrid made it three wins from three thanks to a double from in-form striker Diego Costa in a 3-0 victory at Austria Vienna, leaving the Spanish side on the brink of the last 16 already to continue its brilliant start to the season.
Chelsea claimed the performance of the night by crushing Schalke 3-0, with striker Fernando Torres also scoring twice to put the 2012 champions top of Group E.
Back from a thigh injury, Messi scored from close range to cancel out Robinho's opener for Milan and keep Barca in charge of Group H on seven points, two ahead of the Italians.
Robert Lewandowski grabbed an 82nd-minute winner for Dortmund, last season's beaten finalist, at Arsenal in Group F to bring the English team down to earth after a flying start to the Premier League and in Europe.
They are joined in a three-way tie on six points by Napoli, which won 2-1 at Marseille to condemn the French side to a third straight loss.
There were also first wins of the group stage for Celtic and Zenit St. Petersburg while Basel drew 1-1 at Steaua Bucharest.
Milan and Barca were meeting in Europe's top competition for the seventh time in three seasons, so it was perhaps no surprise to see the teams cancel each other out.
There was no shortage of stars on show at the San Siro and two of them combined for Milan's opener, Robinho exchanging passes with Kaka before slotting past Victor Valdes.
However, Milan has never been able to handle Messi — the Argentina forward has now scored six times against the Italians — and he equalized after collecting Andres Iniesta's pass, evading Kevin Constant and shooting into the bottom corner.
The teams meet again in two weeks' time, with Barcelona knowing a victory would put them on 10 points and close to the knockout stage.
Celtic is two points behind Milan after beating Ajax 2-1 thanks to goals by James Forrest and Beram Kayal in a 10-minute spell either side of halftime.
Ajax grabbed a consolation goal through Lasse Schone in second-half stoppage time, by which time Celtic had been reduced to 10 men after Nir Biton was red-carded in the 87th minute.
Arsenal's first loss since mid-August, on the night of manager Arsene Wenger's 64th birthday too, was sealed by Lewandowsi's unforgiving finish eight minutes from time at Emirates Stadium.
Back in London for the first time since losing last season's final to Bayern Munich in May, Dortmund went ahead through Henrikh Mkhitaryan in the 16th minute only for Olivier Giroud to equalize just before the break.
Jose Callejon and substitute Duvan Zapata were the scorers for Napoli at the Stade Velodrome, with Andre Ayew netting for Marseille four minutes from time.
Atletico, level on points with Barca at the top of the Spanish league, is the only team in the four groups who played on Tuesday to have three straight wins after Costa added to the opener scored by Raul Garcia in the Austrian capital.
Diego Simeone's side is five points clear of Zenit, which beat FC Porto 1-0 thanks to Aleksandr Kerzhakov's goal five minutes from time.
Porto had done well to nearly hold out for a draw after seeing Hector Herrera sent off for two yellow cards after just six minutes.
In Group E, Torres marked his 100th start for Chelsea by scoring in the fifth and 69th minutes, with Eden Hazard completing an unexpectedly easy win against a Schalke team that led the group at kickoff.
"If you do garbage, then you have to clean it up and we cleaned it up," said Chelsea manager Jose Mourinho, referring to his team's home defeat to Basel on the opening matchday. "We've got two matches at home so now we are in good condition to qualify and we'll try to finish top."
Chelsea is ahead of Schalke on goal difference, with Basel two points back after conceding a late goal by Leandro Tatu to draw at Steaua, which claimed a first point in group play.