The Nigerian forward was unable to find the net and received a caution in the 16th minute of the match, marking Bay FC’s second defeat since joining the league.
Oshoala had previously scored Bay FC’s only goal in their inaugural league appearance.
In contrast, Alozie, usually a right-back for Nigeria, played a pivotal role for Houston Dash partnering with Amanda West upfront.
Their dynamic duo troubled the hosts, leading to Diana Ordonez scoring a brace, with substitute Havana Solaun securing the winning goal in added time.
Both Oshoala and Alozie are anticipated to reunite for Nigeria’s Super Falcons in a crucial Olympics qualifier against South Africa.