In truth, Pompey were unlucky to lose as they were bright throughout but the hosts' brilliant start to the season continued as Morais' 62nd minute cross beat everybody before drifting in.
Stevenage went ahead in the 14th minute when Lucas Akins won the ball on the right wing before his cross allowed an unmarked Morais to head in.
Portsmouth came close early in the second half when Bondz N'Gala's weak backpass was seized on by Wes Thomas, who rounded Arnold, but Stevenage captain Mark Roberts bailed out his partner by clearing off the line.
But the visitors deservedly drew level when Jon Harley took a pass from Brian Howard before placing a fine shot into the bottom corner from the edge of the area.
However, Morais claimed the winner when, after taking a short corner from Luke Freeman, his cross drifted past N'Gala before nestling in the far corner.