Surgical removal of mandibular third molars is associated with non-infectious postoperative complications, including pain, swelling, trismus. Intraoral drains are noteworthy because of their ease of application, availability, and effectiveness. This study aimed to evaluate the use of latex and calcium–sodium alginate mouth flat drains on the severity of postoperative complications such as pain, trismus, and edema after surgical removal of mandibular third molars. Ninety patients who underwent surgical removal of wisdom teeth were studied. The patients were divided into three groups. Group A—with a latex flat drain, group B—with a sodium–calcium alginate (Kaltostat) flat drain, and group C—with a wound closed with knotted sutures. Patients were assessed for pain on a VAS scale every day from surgery to postoperative day 7. Before the procedure and on postoperative days 1, 2, and 7, the pain level, edema, and trismus were measured, respectively. Intraoral drainage with a flat drain after mandibular third molar removal does not significantly reduce pain, as measured by the VAS scale, or postoperative swelling, as measured by lines between craniometric points. Intraoral drainage with a latex drain after mandibular third molar removal does not significantly reduce trismus, while intraoral drainage with a calcium–sodium alginate drainage bag significantly increases trismus.