The former child star, best known for playing the lovable Punky Brewster, also invited Nicole Richie and stylist Rachel Zoe to her themed party in Los Angeles' Hollywood Hills.
A source tells Us Weekly magazine that Moore and Alba were "jamming like crazy on the dancefloor" to '80s music, while pop icon Debbie Gibson showed up to play a medley of her hits.
In a post on her Twitter.com page after the event, Frye wrote, "Feel beyond blessed for the amazing people in my life that make me smile and are not afraid to embrace a passion for the 80s!"
Alba also posted several photos from the event, and tweeted to the birthday girl, "Thank you Soleil for inviting us to your rad '80s bday (sic) party! We had a blast and my mom's 80s pose was in full effect."