Cody Zeller also netted 17 points as the Hoosiers (5-0) continued a streak of double-digit victories to start the season.
Also reaching double figures for Indiana were Yogi Ferrell (14 points) and Victor Oladipo (12).
The Hoyas (3-1) got a game-tying basket from Otto Porter in the closing seconds but couldn't find the range in extra time, sustaining their first loss of the season.
Marcel Starks paced Georgetown with 20 points and Porter finished with 15 in the setback.
Costly malfunction causes beer flood at Boston-area brewery
Video of Victoria’s Secret models trying to 'twerk' hits Instagram