The win allowed Barcelona to claim Group F and advance to the last 16 knockout stages of European club football's most prestigious competition for the 13th consecutive season.
Messi, who made his senior debut for Barcelona on 16 October 2004 against Albacete, also set up goals for Luis Suarez and Antoine Griezmann to take his tally up to 237 assists.
Wonder
"He was incredible," said Barcelona coach Ernesto Valverde. "It's all about what he does and when he does it. It was a performance to put us through."
Jadon Sancho scored a late consolation for the visitors who face a fight with Inter Milan to take the runners-up spot.
Dortmund will have to beat Slavia Prague at home in a fortnight's time while relying on Barcelona to avoid defeat at the San Siro.
"We got the most difficult group in the competition in my opinion," said Valverde. "We are through with a game to spare, first in the group, and for the players that means a lot."
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