The committee's vote is non-binding but marks the last formal stage before the full Senate votes Wednesday on starting a trial and suspending the leftist president.
With a 'yes' vote almost certain, Rousseff is preparing to step aside for up to six months while her trial takes place, plunging Brazil into ever deeper political infighting.
As soon as Rousseff is suspended Vice President Michel Temer, a center-right politician whose party recently broke off its shaky alliance with Rousseff's Workers' Party, would become interim president.
The impeachment is based on accusations that Rousseff made illegal accounting maneuvers to mask the depth of Brazil's economic troubles during her tight 2014 reelection victory.
The country's first female president says the charges are trumped up to turn the impeachment process into a coup d'etat. She has vowed to resist to the end.
While Rousseff fights for her political survival, both her closest allies and some of her most bitter enemies are being sucked into an ever deepening corruption scandal centered on state oil company Petrobras.
Cunha was one of Brazil's most powerful political operators and allied to Temer. His probable replacement in the speaker's post is another lawmaker accused of participating in the Petrobras embezzlement ring.
Temer himself is not being probed in the Petrobras affair, the chief prosecutor said this week, despite allegations made against him by a key witness in the government's case.
However, in yet another twist yesterday it emerged that Temer could be barred from participating in any elections for eight years because he has been found guilty of violating campaign finance rules. The ban would not affect Temer's ability to take the presidency next week since no election is involved.