How did Luthien defeat Sauron with such ease?

She didn't. Huan did. All Luthien did was make Sauron stumble. And then Huan, a Maia, took up the battle.

So great was the horror of his approach that Huan leaped aside. Then Sauron sprang upon Luthien; and she swooned before the menace of the fell spirit in his eyes and the foul vapour of his breath. But even as he came, falling she cast a fold of her dark cloak before his eyes; and he stumbled, for a fleeting drowsiness came upon him. Then Huan sprang. There befell the battle of Huan and Wolf-Sauron, and howls and baying echoed in the hills, and the watchers on the walls of Ered Wethrin across the valley heard it afar and were dismayed. But no wizardry nor spell, neither fang nor venom, nor devil's art nor beast-strength, could overthrow Huan of Valinor; and he took his foe by the throat and pinned him down. Then Sauron shifted shape, from wolf to serpent, and from monster to his own accustomed form; but he could not elude the grip of Huan without forsaking his body utterly. Ere his foul spirit left its dark house, Lúthien came to him, and said that he should be stripped of his raiment of flesh, and his ghost be sent quaking back to Morgoth; and she said: ‘There everlastingly thy naked self shall endure the torment of his scorn, pierced by his eyes, unless thou yield to me the mastery of thy tower.’

(Silmarillion)

As you can see, Sauron's direct attack did seem to afflict Luthien; only her cloak and Huan seem to have saved her.

At the end, Luthien is simply threatening Sauron with disembodiment (effected by Huan) unless he yields up the tower. Since he concedes, Huan and Luthien let him go and he escapes (relatively) unscathed, with just a throat-wound that drips blood on the trees.