His compatriot Varun Singh Bhati clinched the bronze medal in the same event here on Friday night.
While Thangavelu made a leap of 1.89 metres, Bhati jumped his personal best of 1.86 metres to finish third.
Sharad Kumar, the other Indian in the fray, finished at the sixth position.
The US's Sam Grewe bagged the silver medal.
This was the third gold medal for India in the history of the Paralympic Games.
Swimmer Murlikant Petkar had won India's first gold at the 1972 edition while Devendra Jhajharia had clinched the second gold by winning the javelin event at the 2004 Games.
The event witnessed a fierce contest with six of the 12 athletes clearing the 1.74m mark in their first eight attempts.
But Thangavelu became a part of the leading group after his 10th attempt when he cleared the 1.77m mark along with Lukasz Mamczarz of Poland, China's Zhiqiang Zhing and Kumar.
He then went into the lead along with Bhati as both managed to clear the 1.83m mark.
Kumar however, could not improve his performance and eventually crashed out of medal contention.
Grewe pushed Thangavelu and Bhati to the joint second position by clearing 1.86m to grab the top spot.
But both Indians made a strong comeback by equalling the height to share the pole position.
Thangavelu eventually made sure of the gold with an effort of 1.89m in his final attempt while Grewe and Bhati finished with best efforts of 1.86m.
Both Thangavelu and Bhati are in line for rich financial rewards as the Sports Ministry had earlier announced that the Indian gold medallists from the Paralympic Games will be awarded Rs.75 lakh each, the silver medallists will get Rs.50 lakh while Rs.30 lakh will be given to the bronze medallists.
Prime Minister Narendra Modi and Congress President Sonia Gandhi took to social media platform Twitter to congratulate Thangavelu and Bhati on Saturday.
"India is elated! Congratulations to Mariyappan Thangavelu on winning a gold and Varun Singh Bhati for the bronze at the Rio Paralympics," Modi tweeted.
Defining the victory as an 'extraordinary achievement' Sonia Gandhi said: "History has been created today. Outstanding lives and games of these athletes will inspire generations to come."
Bollywood stars Aamir Khan and Anushka Sharma also congratulated Thangavelu on his achievement.
"Congratulations Mariyappan! You have done India proud. Thank you. Love. A," Aamir tweeted.
Anushka posted: "Congratulations Mariyappan Thangavelu and Varun Singh Bhati on the absolutely stellar performance and on creating history... Paralympics".
