The 26-year-old, who moved from Panathinaikos on loan in the January transfer window, opened scoring for the hosts inside the Estadio Nuevo Los Cármenes on 38 minutes.
He received a header from Adrian Ramos and shot a low left-footed volley into the side of the net that easily beat goalkeeper Fernando Pacheco.
Wakaso celebrated the goal with aplomb, and ran towards the far side with arms spread out mimicking an aeroplane in flight.
Granada doubled their lead in the second half via Isaac Cuenca whose shot from the edge of the box once again left the goalkeeper stranded.
Alaves notched one back on 57 minutes when Victor Camarasa rebounded his own header after goalkeeper Guillermo Ochoa had stopped the first attempt.
The victory moved Granada up to 18th spot, still in relegation zone, but with hopes that they could escape it at the end of the season.
Coach Lucas Alcarez had expressed hope in Wakaso’s coming as it gives his team ‘dynamism, speed and intensity’ to fight for survival.
He grabbed an assist in the 4-1 win against Real Betis last month and has now played four times for the Nazaries since the end of the Africa Cup of Nations.