Patrice Neveu's side took a slender 1-0 advantage into Sunday's second leg of their preliminary qualifying tie in Curepipe thanks to Adama Ba's goal in Nouakchott last week.
And Demba Sow all but assured their place in the next round by striking seven minutes before half-time.
Moulaye Ahmed rounded matters off in injury time to take Mauritania into next week's second qualifying phase draw and one step closer to a place in the 2015 finals, which will be held in Morocco.
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