The left-handed Indian needed two hours to edge past American Thomas Shubert 6-4 7-5 in the second round of the hard court event.
Jeevan will now fight it out with Japanese sixth seed Gengo Kikuchi.
However, Jeevan could not make it two wins in a day for the second time in a row as he and his Taipei partner lost 6-7(5) 3-6 to Japanese pair of Yuuya Kibi and Tomohiro Masabayashi.
Under testing conditions, Shubert took a 3-1 lead in the second set but the Indian made it 3-3 and then 5-5. Again when Shubert was serving to stay in the match, Jeevan broke him.
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"He was a good player in College. It was a tricky second round, I am happy to be through," Jeevan said.
Meanwhile, Neeraj Elangovan lost both his matches.
He lost the singles second round 4-6 2-6 to Korean eighth seed Woong-Sun Jun. Later partnering Shubert, Neeraj gave a tough fight to top-seeded Japanese pair of Takuto Niki and Bumpei Sato before losing 7-6(5) 2-6 4-10 in the quarter-finals.
In the doubles, Ramkumar and his second seed teammate Ryan Agar from Australia lost 4-6 4-6 to seasoned Sanchai Ratiwatana and partner Wishaya Trongcharoenchaikul.
Ramkumar and Ryan saved two match points at 2-5 and another at 4-5 but the Thai pair clinched the issue on their fourth match point.