The 26 year-old arrived in Sochi as the red-hot favourite, having already captured the large hill world title and leading the way in the World Cup series.
He claimed victory at the RusSki Gorski Ski Jumping Centre with jumps of 105.5m and 103.5m, for a total of 278 points.
That gave him a 12.7-point advantage over second-placed Peter Prevc of Slovenia, with Norway's Anders Bardal winning bronze on 264.1 pts.
"In the morning I had serious health problems, and I thought I was not going to jump,” revealed the newly crowned champion, Poland's first ski jump gold medal winner since Wojciech Fortuna took gold at Sapporo in 1972.
“I didn't expect to gain such a big advantage ahead of the second place but I just did what I'm capable of doing," he added.
"Both of my jumps were fantastic and I'm really happy that my jumps gave me that gold medal."
Going for the double
Stoch now has an Olympic double firmly in his sights. “I really want to repeat it at the large hill. But once again I'm not set to do anything unusual. I will just do my work and enjoy ski jumping. Hopefully, it will be enough for one more win here.”
Prevc, who is second to Stoch in the World Cup, took the silver with 265.3 pts, and was delighted to be joining the Pole on the podium.
“It's great to win the Olympic medal, I'm happy,” said the Slovenian. “Nobody could stop Kamil as he was the best. He jumped without any mistakes and won deservedly. He produced an amazing performance.”
Switzerland's Simon Ammann, 32, who came to Sochi as the reigning champion at both normal and large hills, which he won in 2002 at Salt Lake and in 2010 at Vancouver, failed to earn a record fifth Olympic gold finishing in 17th.
Meanwhile, current World Cup champion Gregor Schlierenzauer of Austria saw his challenge ended by a first round jump of 96m that left him in equal 18th at the halfway stage, and he could only finish 11th overall.
Triple Olympic gold medallist Thomas Morgenstern of Austria finished 14th.