After a huge wins in Highgarden and King's Landing last week, Cersei goes into "The Spoils of War" confident. Too confident, actually. Maybe it's all the wine. With a few wins against Daenerys, the Iron Bank's support, and the woman who murdered her daughter rotting in a dungeon, Cersei is blinded by her victories and forgets the fact that Daenerys has dragons and could attack any time.
The Dothraki go into their first fight in Westeros confident, and they win easily. Drogon definitely helps, but their brutal way of combat helps them defeat the Lannister forces.