But it was disappointment for another Indian athlete Sharad Kumar who failed to finish on the podium.
Thangavelu won the yellow metal with his best jump of 1.89 metres, while Bhati's best effort of 1.86m fetched him the bronze.
The silver medal in this event went to USA's Sam Grewe who also registered the same mark of 1.86 metres.
But it was heartbreak for Kumar, who led the pack at one stage after clearing hurdles of 1.55m and 1.60m. His best jump, though, was only 1.77m which placed him at the sixth position.
The event witnessed huge competition as six out of the 12 para athletes cleared the 1.74m mark in their first eight attempts.
In his 10th attempt, Thangavelu jumped 1.77m successfully, along with three others Poland's Lukasz Mamczarz, China's Zhiqiang Zhing and countrymate Kumar.
In the later stages with the contest being reduced to only three competitors, Bhati set the tone with a jump of 1.83m mark along with Thagavelu.
However, just when it looked like India would fetch a gold and a silver, the American cleared 1.86m to grab the top spot but the Indians also equalled the height to make it even.
Eventually, in a nail biting finale, Thangavelu grabbed the top honours by finishing with a jump of 1.89m.