In 1987, the 18-year-old Einikis arrived at Žalgiris to replace his injured teammate Arvydas Sabonis. He established himself as a strong and aggressive defender, an excellent center and a surprisingly accurate three-point shooter. When Sabonis left Žalgiris, Einikis continued his career as a starter. In 1995, he left for Avtodor Saratov. After dominating with Avtodor, Einikis moved to CSKA Moscow. After 2 moderate seasons, he moved to Idea-Slask, where he averaged 9 points per game and 4.4 rebounds per game in 22 minutes of Euroleague action. He moved back to Zalgiris, contributing more to the team. During the last years of his career his averages fell drastically; however, he helped Lietuvos Rytas to win Uleb Cup in 2005. He retired after the 2005-06 season. In 2009 he returned to professional basketball and played for Naglis-Adakris. After 2009-2010 season he retired second time.
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In 2008, Einikis participated in altercation with a night club's staff, yelling insults, threatening physical harm and refusing to leave the club. He and his friend were fined with 3,000 Litas.
After the incident, Einikis was spotted leaving the club in his car Volkswagen Touareg. Because he had lost his license a year ago after his involvement in a hit and run accident, he was fined with an additional 2,500 Litas. During the accident, it was speculated that he was on cocaine. The police discovered cocaine powder in his car.
In 2011, Einikis, heavily intoxicated, with 5.11 per milblood-alcohol concentration, went to his friend's house and threatened to kill her by setting her house on fire. He was later arrested and charged with threats of arson and assault.
He married his longtime friend Jurgita in July 2012. Later that month, however, he, while under the influence of alcohol, physically assaulted his wife. He is currently incarcerated pending trial.