Siem finished with an eight-under-par total of 276 to claim his first European Tour win since the 2004 Dunhill Championship after a final round of 67 on the par-71 course.
Molinari had enjoyed a late surge that saw him recover from an early double bogey on the first hole to hit nine birdies, stirring up the local crowd and putting pressure on Siem.
The windy conditions didn't help the 31-year-old German's cause but Siem did well to hold his nerve and stay focused with birdies in the 14th and 15th to stay ahead of the Italian.
Frenchman Raphael Jacquelin took advantage of a late stumble from Siem's playing partner Henrik Stenson to claim third place on six-under.
Swede Stenson triple bogeyed the last hole, ending the tournament tied for seventh having teed off on the 18th challenging for the title at seven-under.
Britain's David Howell, David Lynn and Ian Poulter finished joint fourth on five-under.
"I'm so happy," said Siem. "It means a lot to me. So many tournaments I kind of destroyed already this year, I'm so happy I got it done in the end.
"I was very nervous. The last stretch is one of the toughest stretches we have on tour.
"I made great golf shots. I hit it very close on 15, made a good shot on 16 and on 17 I even hit the flag.
"I stayed very calm. It means so much to me to win after that long stretch. It's all about winning in the end."