Terceros converted in the 45th minute for Bolivia, who defeated the Carlo Ancelotti's Selecao at home for the first time since 2019.
The playoff tournament will involve six nations and will be played in March's international window to decide the last two spots for the World Cup to be played next year in the United States, Canada and Mexico.
Bolivia are aiming to qualify for their fourth World Cup and first since 1994.
Uruguay, Colombia and Uruguay were the most recent South American teams to qualify for next year's finals last week and the final round of the qualifiers was meant to decide the team to advance to the international playoff.
The Colombians, who finished in third place in the qualifiers, helped Bolivia's cause by rolling past Venezuela 6-3 with a big night from striker Luis Diaz, who scored four goals.
Diaz scored in the 42nd, 50th, 59th and 67th minutes, while Yerry Mina did so in the 10th and Jhon Cordoba in the 75.
Also on Tuesday, Enner Valencia scored a spot kick and Ecuador defeated reigning champions Argentina 1-0.
The 35-year-old converted in the 45th minute for the Ecuadorians, who finished second in the standings with 29 points behind the Argentinians' 38.
Lionel Messi, who played his last official match at home last Thursday, did not suit up.
Uruguay finished the qualifying tournament with a scoreless draw against Chile, and Paraguay defeated Peru 1-0.
