The top seed, known as the "Rafa Nadal" of badminton in Spain for her tenacity and fierce left-handed game, closed out a 19-21 21-12 21-15 victory over the 21-year-old Sindhu who was majestic in her Olympic debut.
"I'm very excited, I don't know how I'm feeling now but it is amazing that my dream has come true. I just had to believe in myself," Marin told reporters.
"It is more than a medal because of everything behind the medal. I have the best team behind me, they helped me a lot and were amazing."
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Letting out a blood-curdling shriek with every winning point, the Spaniard was jeered by spectators at the Riocentro in a nerve-shredding deciding game as she pushed the bounds of good sportsmanship with constant stalling tactics.
But the ruthless 23-year-old got the job done, charging away to set up six match points and sealing it on the second with an imperious smash down the line that her opponent did well to get a racquet to.
Flag-waving Spanish fans jumped up and down as twice world champion Marin pumped her fists and bellowed in triumph, having survived a huge scare.
The flamenco-trained dancer from Andalucia beamed dry-eyed as she accepted the medal on the podium but wept freely as Spain's flag rose in the arena to the sound of the national anthem.
Roared to the finish by Indian fans, Sindhu will bow out with huge acclaim as her nation's first woman ever to win silver and having clinched the country's second medal at these Games.
It was also India's second medal in badminton, coming four years after compatriot Saina Nehwal grabbed a bronze in the same event in London.
Japan's Nozomi Okuhara won the Rio bronze in a walkover after her Chinese opponent, the 2012 singles champion Li Xuerui, pulled out of their playoff with a serious knee injury.
Sindhu, coached by the same man who took Nehwal to her London medal, was under huge pressure from the nation of a billion people to end India's agonising wait for a Rio champion.
Despite bringing their biggest ever delegation, about 50 percent stronger than London where they won six medals, India had only celebrated a solitary bronze won by freestyle wrestler Sakshi Malik on Wednesday.
"I thought it would be a gold but never mind, I got a silver," the Hyderabadi shuttler said.
"I never thought I would make it to here."
(Editing by Jan Harvey and Nina Chestney)
