Nagornyy, 22, earned the first individual world title of his career having claimed bronze behind Dalaloyan in Doha last year.
Nagornyy finished 1.607 points ahead of Dalaloyan while Ukraine's Oleg Verniaiev, who had surgery on both ankles in January, took bronze.
Dalaloyan paid the price after a rare mistake on his landing from the vault saw him finish 18th in the discipline.
China's Xiao Ruoteng, the 2017 world champion and 2018 silver medallist, finished fourth after a fall on the horizontal bar left him in 21st place in that event.
Nagornyy had the highest score in two of the six events - the vault and rings - and finished in the top three on the floor and parallel bars.
It was his second gold medal in Stuttgart after Russia won the team competition on Wednesday.
Japan's Olympic champion Kohei Uchimura, who has won the all-around world title a record six times, is missing from Stuttgart after struggling for form after injury.
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