Former Barcelona, Inter Milan and Chelsea man Eto'o, 36, put Antalyaspor ahead after just four minutes, and then restored his side's lead on 65 minutes.
Mustapha Yatabare had brought former Western Sydney Wanderers coach Popovic's side back on level terms only minutes earlier.
Karabukspor were unable to find a way back into the game after Eto'o's second, with their cause not being helped by Ceyhun Gulselam's 67th-minute red card.
The loss leaves Popovic's side in 16th place on the Super Lig table in the relegation zone.