The 15-year-old led from start to finish to touch in 1:05.47 as she held off a fast-finishing Rebecca Soni, the Beijing silver medallist. Japan's Satomi Suzuki claimed the bronze.
An emotional Meilutyte told BBC Sport afterwards: 'I can't believe it. It's too much for me.'
Meanwhile, USA's Matt Grevers set a new Games record as he claimed gold in the men's 100m Backstroke.
Grevers clocked 52.16, with compatriot Nick Thoman (52.92) claiming the silver and Japan's Ryosuke Irie (52.97) bronze.