The early goal was also the only one of the match and Milan thus won 1–0.
Asllani was replaced in the 78th minute.
The goal was Asllani's seventh in the league, which places her in joint second place in the shooting league.
Inter's Tabita Chawinga tops the charts with nine hits.
Chawinga won the shooting league in the ladies' league in 2017 with 26 goals when she represented Kvarnsvedens IK.
Milan have mixed and given in Serie A this season.
The victory means that the team is fifth with 19 points, eleven behind league leaders Roma.