Hosts USA attracted a sell-out 18,467 crowd on Thursday night for a 4-2 defeat of Japan in the 2018 Tournament of Nations, which Australia had kicked off with a 3-1 victory over Brazil.
Morgan’s opener was quickly cancelled out when Mina Tanaka’s effort was deflected in off Emily Sonnett, but the latter then set up Morgan to restore the advantage 10 minutes later.
Morgan completed her hat-trick in the second half and Megan Rapinoe added a fourth before Moeno Sakaguchi pulled one back.
Australia scored two first half goals from corner kicks, the first an own-goal by Poliana off a Elise Kellond-Knight delivery, the second headed home by Tameka Butt.
Sam Kerr effectively sealed the victory with a powerful finish from a 50th-minute counter-attack but Brazil got a consolation when Marta set up Debinha to net.
The second round of games are at East Hartford in Connecticut, on Sunday, where the US face the Matildas and Brazil take on Japan.