Lowry and Rock each closed with a 1-under-par 71 for a total of 17-under 271 in regulation play.
Both players parred the first extra hole and birdied the second. On the third, Lowry won with a 1-foot par putt after Rock missed his attempt at par.
"I can't believe it. This is going to take a long time to sink in," Lowry said.
Johan Edfors (71) placed third at 15-under 273. Marc Warren (68) and Nick Dougherty (69) shared fourth at minus at 275.
Lowry said he would soon make his decision to turn professional.
"I know my life is about to change forever," he said.
Lowry became the third amateur to win on the European Tour. The others were Danny Lee, earlier this season, and Pably Martin.