The success gave joyous Spanish fans in the Zagreb Arena plenty to cheer about after several lean years, including a fifth-place finish in last year's world championship which came on the back of missing out on the 2016 Olympic Games.
Sweden, who had defied the odds to reach the final, led 14-12 at halftime but the Spaniards turned the match on its head with an 8-1 streak early in the second half with their stand-in goalkeeper Arpad Sterbik pulling off some crucial saves.
Earlier on Sunday, world champions France beat Denmark 32-29 to win the bronze medal and get some revenge on the Danes for losing the 2016 Olympic final to them
The Swedes made a bright start and led by three goals in a fast-paced opening period, with their keeper Mikael Appelgren racking up 11 saves to frustrate Spain.
But the Spaniards looked more like the team that won the 2013 world title as they overran their rivals after the break, capitalising on the 38-year old Sterbik's acrobatics and a flurry of Swedish turnovers.
Sweden's trademark fast breaks, their most lethal weapon throughout the competition, dried up in the second half of the final and Spain started rifling in goals from all angles to carve out a 25-17 lead with eight minutes left.
Ferran Sole and David Balaguer scored five goals each for Spain while backs Raul Entrerrios and Alex Dujshebaev chipped in with four apiece.
French playmaker Nikola Karabatic made amends for a poor last-four display against Spain with nine goals from 11 shots to lead his team's effort against Denmark, who never looked like recovering from a dramatic defeat by Sweden in the other semi-final.
Three of Karabatic's team mates added five goals each to underline a balanced attack which wiped out a heroic solo effort by Denmark winger Hans Lindberg, who netted 12 goals.
(Writing by Zoran Milosavljevic in Belgrade; Editing by Clare Fallon)
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