Delic troubled the world no 3 with his powerful serve, but Djokovic's big-match experience proved decisive. Delic was promoted to the main draw as a lucky loser when Nicolas Kiefer pulled out.
Djokovic will next face Mardy Fish or Marcos Baghdatis.
Meanwhile 3rd seed Dinara Safina advanced to the fourth round with ease. She had an easy victory over Estonia's Kaia Kanepi 6-2 6-2 on Friday, Jan 23.
25th seed Kanepi's poor service was a blessing for Safina. Kanepi made just 40 pc of her first serves and had 28 unforced errors. Kanepi was never able to pressurise Safina and she sealed her victory when Estonian hit a forehand into the end of the 66-minute match.
World no. 3, Safina will now face either 15th seed Alize Cornet of France or Daniela Hantuchova of Slovakia (19th seed).
Top seed women's result
---3-Dinara Safina (Russia) beat 25-Kaia Kanepi (Estonia) 6-2 6-2
---10-Nadia Petrova (Russia) beat Galina Voskoboeva (Kazakhstan) 6-1 (Voskoboeva retired)
---7-Vera Zvonareva (Russia) beat Sara Errani (Italy) 6-4 6-1
---16-Marion Bartoli (France) beat Lucie Safarova (Czech Republic) 3-6 6-2 6-1
Top seed men's result
---8-Juan Martin Del Potro (Argentina) beat Gilles Muller (Luxembourg) 6-7(5) 7-5 6-3 7-5
---19-Marin Cilic (Croatia) beat 11-David Ferrer (Spain) 7-6(5) 6-3 6-4
---3-Novak Djokovic (Serbia) beat Amer Delic (US) 6-2 4-6 6-3 7-6
OneIndia News (With inputs from Agencies)