Two years later, Matas was chosen to travel with the U.S. Yellow Fever Commission to Havana to serve as laboratory assistant and interpreter. There he met Dr. Carlos Finlay, the first to suggest the mosquito as the yellow fever vector.  Matas was, for a time, the sole supporter of the theory.

Matas' first landmark paper was published in 1885; in it, he unequivocally defined the cecum and appendix as intraperitoneal.  Subsequent milestones include his use of spinal anesthesia in 1889, the first in the United States, his development of the intravenous drip, and his use of endotracheal intubation with positive-pressure ventilation to dramatically improve the safety of thoracic surgery.

His most renowned achievement, however, was his development of the intrasaccular technique for the surgical treatment of aneurysm.  Previously, surgical treatment of aneurysm was limited to proximal and distal vessel ligation.  Matas' technique, initially an improvisation to control bleeding from a brachial artery aneurysm fed by numerous collaterals, involved opening the sac and obliterating the ostia of the collaterals from inside; it was later refined to preserve the patency of the parent artery in favorable cases.

Matas' career was one of distinction from the outset: at 23 he was appointed director of the New Orleans Medical and Surgical Journal, and at 35 he became chairman of Tulane's Department of Surgery.  At 48, gonococcal keratoconjunctivitis, acquired in the operating room, necessitated enucleation; Matas subsequently became fond of remarking on what a great deal "we Cyclopeans can accomplish in a binocular world."  Indeed, Matas continued his surgical practice and civic and academic pursuits until the age of 92, five years before his death.