The previous nine-goal mark was set by Ghana in a 1974 World Cup qualifier and equalled by Libya in a 2006 tie.
Rwanda fell just short of the record eight-goal margin for a single match set by the Democratic Republic of Congo in a 2002 qualifier and later equalled by Libya.
Guinea-Bissau, once minnows but qualifiers for the last two Africa Cup of Nations tournaments, fell behind at home after 11 minutes to an aggregate-tying goal from Sao Tome.
The visitors, whose “The Falcons and True Parrots Team” nickname must rank among the most eye catching in football, retained the second leg lead until midway through the second half.
Joseph Mendes, who equalised in Bissau on 66 minutes, was yellow carded for taking his shirt off when celebrating, and scored again to give Guinea-Bissau a 2-1 victory.
The “Djurtus” (wild dogs) progressed 3-1 on aggregate to keep alive the seemingly improbable dream of coach Baciro Cande, who believes a team ranked 123rd in the world can qualify for Qatar.