Brazil have not been at their brilliant best in the competition, thus far, and sit fourth in the table on the back of a disappointing 4-1 reverse to arch-rivals Argentina, last time out.
Cunha scored his first senior international goal in that huge fixture, in what was his 13th cap for the Selecao, but only his fourth start.
Carlo Ancelotti has replaced Dorival Jnr as coach and said: "These two matches are very important. I have tried to bring in players who are ready and prepared to help the team win."
Former Red Andreas Pereira is also in the squad with the first match, away to Ecuador, which is always difficult due to the altitude, at 00:00 BST on Friday.
The Paraguay clash follows in the early hours of Wednesday morning UK time.