Portsmouth started the game well, pinning Southampton deep in their half as a boisterous Fratton Park crowd roared their team on.
But it was the Saints who had the best chance in the opening exchanges as Adam Armstrong was played in behind by Azaz but could not finish past Schmid, who made a crucial save with his legs.
Moments later they came close again with Armstrong sliding on to the end of a cross and forcing Schmid into another big stop from close range.
Pompey had a claim for a penalty kick after 25 minutes when Ibane Bowat went down in the box after challenging for the ball, but referee Lewis Smith waved away the appeals.
Scienza then fired Southampton into the lead in the 57th minute after Azaz played him clean through on goal down the left-hand side.
The Brazilian just had Schmid to beat and he did so with ease, finishing with his right foot before wheeling off in celebration.
Tensions spilled over with about 20 minutes remaining as Flynn Downes and Zak Swanson squared up to each other after a heavy challenge by the Saints midfielder, creating a melee involving a number of players.
Portsmouth managed to find an equaliser in the 77th minute as Adrian Segecic's corner kick was deflected across goal by a Southampton player before Adams jumped the highest to head the ball into the goal from a few yards out.