Nigeria kept pace with Group B leaders Guinea, who they will host in the final qualifying match next month. The two sides have 10 points but Guinea were playing Ethiopia later on Sunday.
Captain Yobo scored from a John Obi Mikel corner in the 68th minute and Obinna hit home a long-range shot for a second eight minutes later in a result that will have provided much relief for the beleaguered Nigerians.
Nigeria coach Samson Siaisa, who earlier this week criticised his top players for a casual attitude towards national team duty, dropped long-standing first-choice goalkeeper Vincent Enyeama who had led a team sit-in over dissatisfaction with travel arrangements.
Nigeria now travel from Madagascar to Bangladesh where they play Argentina in a friendly on Tuesday.