Lowry, who missed a three-foot putt to win on the last hole of the fourth round as he and Rock finished tied at 17-under 271, finally sealed victory on the third extra hole.
"I don't know how I missed that putt on the 72nd. I just pulled it," Lowry said.
They halved the first two tries of the playoff on the par-5 18th, but Lowry made par on the third attempt as Rock missed the green with his third shot and took three more to get down.
Lowry became only the third amateur to win on the European Tour. Danny Lee of New Zealand won the Johnnie Walker Classic in February and Pablo Martin of Spain took the Russian Open in 2007.
He is the first amateur to win in his debut appearance.
As he left the green, Rory McIlroy had a brief word in his ear. "He just told me 'Don't worry. Just keep it going,'" Lowry said.
In the playoff, Rock missed a 10-footer for victory on the first hole but made a 9-footer to match Lowry's birdie at the second try.
Both missed the fairway on the next effort and were short of the green, but Lowry pitched to 20 feet and two putted. Rock cleared the green, pitched to seven feet and missed.
"I can't describe how I feel. I had an invite to play here and just wanted to make the cut. But after I shot 62 Friday, I felt I could win," Lowry said.
McIlroy, who tied 45th in a disappointing week, was delighted for his friend.
"This was awesome,"he said. "Shane's a great guy and thoroughly deserved this. To have to survive a three-hole playoff was incredible."
Lowry may decide to turn pro immediately. If he does, he can play in this week's BMW PGA Championship at Wentworth.
"I'll have to think about it overnight and talk to a few people," Lowry said.
McIlroy thought he should. "He has nothing left to do as an amateur," he said.
Rock said he was trying to chip in from off the green with his fourth shot on the last hole. "You have to. I thought I needed it to win," he said. "But I hit it too hard."
Sweden's Johan Edfors also shot 71 to take third place at 273. Marc Warren (68) and Nick Dougherty (69) were tied for fourth at 275.
European Ryder Cup captain Colin Montgomerie, in contention after three rounds, soared to a closing 80 to tie for 41st.