Messi doubled Barca's lead after setting up Luis Suarez's opener in the Group F clash at Camp Nou.
Dortmund became the 34th side against which Messi has scored in the Champions League as the Argentina forward surpassed a mark he had shared with Cristiano Ronaldo and Raul.
Messi received a neat pass from Suarez before calmly converting past Dortmund goalkeeper Roman Burki in the 33rd minute.
The 32-year-old only equalled Ronaldo and Raul last month, when he netted in a 2-1 win over Slavia Prague.
Messi also set up Antoine Griezmann for Barcelona's third as they sealed qualification.