The result left Sevilla, the winners of the last three titles in the second-tier Europa League, level on seven points at the top of the section alongside Juventus, who were 1-0 winners at Olympique Lyonnais.
Lyon have three points while Dinamo, the only side of 32 teams in the competition yet to score a goal, have none.
Sevilla missed a string of chances on a slippery surface either side of Nasri's clinical 37th-minute finish, when he poked the ball home from a tight angle after a low cross by Mariano Ferreira.
Nasri, who moved to Sevilla on a year-long loan from Manchester City during the close season, shot wide from a similar position midway through the first half as Dinamo struggled to get out of their own half.
Mariano, Luciano Vietto and Franco Vasquez also came close and the visitors were nearly punished for their misses in the closing stages after Dinamo finally pressed forward.
El Arabi Hilal Soudani, Gordon Schildenfeld and 18-year-old Borna Sosa all came within a whisker of getting an equaliser at the Maksimir stadium but Sevilla held on to their slender lead.
(Writing by Zoran Milosavljevic in Belgrade; Editing by Pritha Sarkar)
