The fifth-seeded Indian needed more than an hour to clinch a 21-15, 12-21, 21-14 victory over his unseeded opponent.
Srikanth will face another unseeded opponent in American Daren Liew in the next round.
The American defeated Misha Zilberman of Israel 21-16, 21-16 in the second round.
The first game was a closely fought see-saw affair before Srikanth clinched four back-to-back points to reach game point at 20-13. Although the Spaniard managed to reduce the deficit, it was not enough to prevent the Indian from taking the opening game.
Abian made a strong comeback in the second game. He went into the break with a narrow 11-10 lead and took the game away from Srikanth immediately after the restart with an awe-inspiring run of seven consecutive points.
The third and decisive game was also a neck-and-neck fight, but Srikanth held his own in the closing stages to clinch the issue.