Boca have not won a league title in Argentina since 2011, suffering one of their least successful periods in recent history – and they are without a league win since November.
Belgrano recovered from conceding the opener at La Bombonera on Sunday to score the next three goals and while Luciano Acosta struck for Boca in second-half stoppage time, the visitors held on to win.
Cesar Pereyra was the key man for Belgrano, setting up Emiliano Rigoni for the visitors' first goal and then scoring himself in the 90th minute to make it 3-1.
Boca took the lead in just the seventh minute when defender Juan Forlin ran onto Juan Sanchez Mino's centring header to nod the ball past Belgrano goalkeeper Pablo Heredia.
The hosts stayed in front until half-time but two minutes after the break Rigoni equalised, running onto Pereyra's lofted pass, holding off two opponents and then finishing with aplomb.
In other results, River Plate drew 1-1 at Rosario Central, Gimnasia La Plata stunned Newell's Old Boys 3-0, Colon defeated Argentinos Juniors 1-0, San Lorenzo trumped Racing Club by the same scoreline and Godoy Cruz won 2-0 over Quilmes.
