Romania are second from bottom in Group D with five points from five games, one place below Bosnia (seven points).
Mutu opened the scoring from close range in the 37th minute before Marica put the game beyond the visitors in the 41st and 55th.
Cristian Sapunaru also missed a penalty for the home team deep into stoppage time.
"It was a very good performance ... I hope this is a new beginning for Romania," Mutu told state television.
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Romania resume their qualifying campaign against bottom team Luxembourg in September while Bosnia entertain Albania on Tuesday.

