The Black Stars recorded a 2-0 win away in Port Louis to qualify for the 2017 AFCON tournament in Gabon.
Stand-in skipper Andre Ayew and Christian Atsu found the net in the second half to hand Ghana another win to keep them undefeated after five matches.
The Stars dominated the tie from start to finish but the Mauritian defence blocked several attempts in the first half.
When the defence was beaten, goalkeeper Kelvin Jean-Louis made several stops to thwart Mubarak Wakaso, Frank Acheampong and Andre Ayew.
His exploits continued in the second half until the 70th minute when Andre Ayew found the net. He received a cross from Baba Rahman but needed to get the ball onto his left foot. He calmly did so and beat two defenders in the process before firing past Jean-Louis.
Five minutes later, Atsu was the beneficiary of another Baba Rahman centre as he connected with his right foot to send the ball into the roof of the net.
Grant made some changes after that with Jeffrey Schlupp and Thomas Partey coming on for Christian Atsu and Frank Acheampong respectively.
The Black Stars saw out the result to get into their sixth straight AFCON since 2006.
Black Stars starting lineup: Razak Brimah; Harrison Afful, Baba Rahman, Jonathan Mensah, John Boye; Muabarak Wakaso, Christian Atsu, Afriyie Acquah; Jordan Ayew, Andre Ayew (captain), Frank Acheampong.
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By: Nathan Quao/citifmonline.com/Ghana