On April 2, 2015, he was selected for the Ideal Team for the 2014–15 ABA League season. Later that month, he helped his team to win the 2014–15 ABA League trophy. He was named the MVP of the ABA League playoffs. In May 2015, he was chosen for the All-EuroLeague First Team.
On June 5, 2015, Marjanović was named the Serbian Super League MVP for the third consecutive season, having helped his team to reach first place in the regular season with a record of 13–1. Crvena zvezda won the 2014–15 Serbian League championship after a 3–0 series victory over Partizan Belgrade.
On July 17, 2015, Marjanović signed a one-year, $1.2 million contract with the San Antonio Spurs. He made his NBA debut on October 30, recording six points and five rebounds in the Spurs' 102–75 win over the Brooklyn Nets. On December 4, he was assigned to the Austin Spurs, San Antonio's D-League affiliate. He was recalled by San Antonio on December 6, and, the following day, scored 18 points on 8-of-10 shooting in a 119–68 win over the Philadelphia 76ers. On December 28, in a win over the Minnesota Timberwolves, with Tim Duncan out injured and LaMarcus Aldridge limited to six points, Marjanović scored 17 points on 7-of-7 shooting in 14 minutes to help the Spurs defeat the Timberwolves 101–95 and extend their franchise-record home winning streak to 27 games (dating to 2014–15 season). Two days later, in a win over the Phoenix Suns, he became the first player in Spurs franchise history to record 12 rebounds in 15 minutes or less. On January 21, 2016, he recorded 17 points and a career-high 13 rebounds in a 117–89 win over the Phoenix Suns. On March 20, he was reassigned to the Austin Spurs, earning a recall two days later. On March 23, he scored a then career-high 19 points in a 112–88 win over the Miami Heat. On April 13, in the team's regular season finale, Marjanović recorded a career-high 22 points and 12 rebounds in a 96–91 win over the Dallas Mavericks.
In August 2015, the San Antonio Spurs prohibited him from playing for the Serbian national team at EuroBasket 2015 due to risk of injury after signs of pain in his left foot, although the Serbian Basketball Federation (KSS) stated that no bone fractures were found.
Marjanović made a cameo appearance as Jānis Krūmiņš in 2015 Serbian sports drama film We Will Be the World Champions. In 2019, he played an assassin named Ernest who quotes Dante's Divine Comedy in the American action thriller John Wick: Chapter 3 – Parabellum and fights John Wick in the New York Public Library resulting in his own defeat and death.