Narimasa was a son of Sassa Morimasa. His elder brother, Sassa Magosuke, gained fame for his role in the First Battle of Azukizaka in 1542, becoming one of the "Seven Spears" of that engagement, but was killed fighting the followers of Oda Nobuyuki at the Battle of Inabugahara in 1556. Narimasa served Nobunaga throughout the latter’s career. He was present at the Battle of Anegawa in 1570, where he was in the rear guard, and fought at Nagashino (1575). In 1575 he was given Komaru in Echizen, where he had recently helped put down rioting Ikko-Ikki, and became a member of the so-called Sanninshu (Echizen Triumvir) along with Maeda Toshiie and Fuwa Mitsuharu.
A veteran of fights against the Kaga monto, Narimasa was tasked with helping to fight the Uesugi and their vassals in [[Etchu province|Etchu] ]in 1580. He was officially given the province the following year and immediately conducted a land-survey there, as well as improving the province's poor flood control system. In 1582 Narimasa and Shibata Katsuie descended on Uzu Castle, the Uesugi’s last major stronghold in Etchu. The lord of the Uesugi, Kagekatsu, dispatched a number of his important retainers to help hold the place. The Oda forces nonetheless prevailed and the loss of the castle, and those important retainers, opened the way for an invasion of Echigo. Nobunaga’s death in June at the hands of Akechi Mitsuhide, however, sent all the Oda generals involved in the war against the Uesugi onto the defensive, with Narimasa adopting a wait-and-see stance while Katsuie hurried to Owari to be heard in the naming of an heir for Nobunaga. When Katsuie and Hideyoshi came to blows towards the ends of the year, Narimasa supported the former, although with little impact on the outcome of the so-called Shizugatake Campaign (1583). The following year he threw in his lot with Tokugawa Ieyasu, the next man to challenge Hideyoshi. The Sasa clashed with Maeda Toshiie at Kanazawa in Kaga province and attempted to reduce Suemori in Noto province but failed. When faced with the approach of Hideyoshi himself in 1585, Narimasa surrendered. He lost Etchu (valued around 100,000 koku) but was spared and was given a fief in Higo in 1587, along with careful instructions regarding how it should be governed. Narimasa evidently ignored Hideyoshi's injunctions and within a year the Higo samurai were in a state of rebellion. Hideyoshi ordered Narimasa to commit suicide as a result. His sons Nobuharu and Nariharu killed themselves as well.
While in the service of Oda Nobunaga, Narimasa had been considered something of an expert in gunnery tactics and consequently commanded arquebus troops in many of the engagements he fought in. Regarding his suicide, some have speculated that Hideyoshi assigned Narimasa to Higo in the understanding that trouble would arise in that place. This would give Hideyoshi an excuse to dispose of Narimasa - which is at any rate what occurred.