Messi took his tally to the season to 14 for the European champions and joined the retired Laszlo Kubala as Barcelona's second highest goal-scorer of all time with 194.
Marseille kept up its perfect start with a 3-0 victory over Borussia Dortmund. The French side leads Group F ahead of Arsenal, which beat Olympiakos 2-1 to become the only one of the four English teams to win this week.
Chelsea was held to a 1-1 draw at Valencia in Group E, a day after Manchester City lost at Bayern Munich and Manchester United was held by Basel.
APOEL Nicosia is the surprise early leader in Group G after drawing 1-1 at Shakhtar Donetsk, while Zenit St.
Petersburg rose to second by beating FC Porto 3-1. In Minsk, Barcelona took advantage of BATE's defensive frailties to record its first Champions League victory since defeating Manchester United in May's final.
An own goal by BATE midfielder Aleksandr Volodko put Barcelona ahead before Pedro Rodriguez headed in the second from David Villa's cross.
And when Pedro's tame cross slipped through goalkeeper Aleksandr Gutor's hands, Messi tapped the ball across the goal-line to send Barcelona in at half time 3-0 up.
Messi claimed his second just after the restart with a strike from inside the area, and David Villa capped the win in the 90th by slotting into the net.
With 14 goals already this season, Messi will have his sights set this season on surpassing Cesar Rodriguez's record 235 goals from 1942 to 1955 for Barcelona.
Barcelona had drawn its Group G opener with AC Milan.
Against Czech side Viktoria Plzen, Zlatan Ibrahimovic netted from the penalty spot at the start of the second half and provided the pass for Antonio Cassano to double the lead the San Siro.
The penalty was awarded when Plzen defender Marian Cisovsky handled the ball inside the area while attempting to mark Ibrahimovic. Cassano then scored with a delicate chip over the goalkeeper.
"It was important to win and get the three points and follow up the match in Barcelona," Milan coach Massimiliano Allegri said. In London, new signings Alex Oxlade-Chamberlain and Andre Santos provided Arsenal goals.
The 18-year-old Oxlade-Chamberlain netted just eight minutes into his European debut, slotting a shot between the legs of Olof Mellberg and to the right of goalkeeper Franco Costanzo.
Andre Santos made it 2-0 in the 20th minute, with Marouane Chamakh returning the ball into his path after an initial cross and sending a low shot inside the near post.
But Arsenal's much-maligned defense soon showed its frailties once again, letting David Fuster pull a goal back with a powerful header when left completely unmarked after a corner.
Arsenal is two points behind Marseille in Group F after Andre Ayew's double and Loic Remy's strike secured the French side''s win over Dortmund.
Chelsea tops Group E despite Roberto Soldado''s late penalty salvaging a draw for Valencia to cancel out Frank Lampard's goal.
Former Chelsea midfielder Michael Ballack scored in Bayer Leverkusen's 2-0 victory over Genk to go a point behind his old club.
In Ukraine, Jadson equalized for Shakhtar Donetsk three minutes after Ivan Trickovski scored for Cypriot visitor APOEL, which has a one-point lead over Zenit in Group G.
Zenit went ahead of Porto on goal difference after Roman Shirokov scored two goals and also set up Danny's tap-in. The Portuguese champions had led in Russia when James Rodriguez scored after 10 minutes.