Yves Kireko gave league runners-up Musongati a second-minute lead at Stade Urukundo in Buye and Derick Kalulika levelled just four minutes later.
There were no further goals in regulation or extra time and Musongati triumphed 5-4 in the shootout.
Spectators were admitted to matches in the east African nation throughout the pandemic and the crowd at the final did not practice social distancing in the packed stands.
Other countries who defied the global pandemic and continued playing top-flight football included Belarus, Nicaragua, Taiwan and Tajikistan.
It was the first domestic trophy won by Musongati and qualifies them for the 2020/2021 CAF Confederation Cup, the African equivalent of the UEFA Europa League.
Le Messager Ngozi, who finished eight points ahead of Musongati to win a second title in three seasons, will be the Burundian representatives in the CAF Champions League.
No Burundi club has won an African competition with Vital'O coming closest by losing the 1992 African Cup Winners Cup final to Africa Sports of the Ivory Coast.
The landlocked country is ranked 43rd in Africa and 149th in the world and secured a place in the Africa Cup of Nations tournament for the first time last year.
Known as the Swallows, the national team lost to Nigeria, Madagascar and Guinea in Group B and were eliminated after the first round.
Meanwhile, another east African nation, Tanzania, last month became the first in the continent to resume playing after stopping in March due to the COVID-19 disease.