The eighth seeded Serb Tipsarevic received treatment on a foot injury and pulled the pin when trailing 6-2 5-1 in the match at Hisense Arena.
The 10th-seeded Almagro advances to his first quarter-final at Melbourne Park in his ninth appearance at the year's first grand slam after making the last eight at the French Open three times.
Tipsarevic had played two successive five-set matches coming into the Almagro clash and said in the leadup that his legs were going to "feel" it.
(Reporting by Ian Ransom; Editing by Patrick Johnston)
- Sports & Recreation