Penge sealed victory on the first sudden-death hole, after his fellow countryman Brown had come back from five shots behind heading into the last round.
"It felt like I was really up against it, but I feel like I managed myself really well and managed to stay solid," said world number 55 Penge.
"I felt good. I was just trying to stick to the same stuff I've been doing for the last six months."
Penge also won the Hainan Classic and the Danish Golf Championship earlier this year in a breakthrough campaign.
The 27-year-old struggled to a two-over front nine to give playing partners Brown and Joel Girrbach hope after starting the day four strokes clear at the top of the leaderboard, but a birdie on the 12th helped him stay in front.
Brown, ranked 102nd, forced added holes with a birdie on the 18th, a short par four.
But Penge turned the tables when they played the closing hole again a few minutes later in the playoff to take the spoils.
Switzerland's Girrbach finished alone in third place on 14-under for the tournament, one shot outside the playoff.
Three-time champion and home favourite Jon Rahm delighted the crowds with a final-round 65 to finish in a tie for ninth.