Sappho's use of invocation can be seen in her "Ode to Aphrodite." Aphrodite was the Greek goddess of love, and it was common in Ancient Greece for lovers to invoke her name in helping them to find love—that's precisely what Sappho does here.
The speaker—generally thought to be Sappho herself—is crestfallen at being rebuffed by the object of her affection, so she prays to Aphrodite to soothe the terrible emotional pain that she's suffering. The goddess responds by appearing to the speaker in a vision, assuring her that, in due course, the woman she so intently desires will pursue her. Even so, Sappho goes on to invoke the assistance of Aphrodite once more, pleading with the goddess to fight as her comrade in all her future battles.