He was leading after the first run but was beaten by home favourite Marcel Hirscher to record the first podium of his career.
It was the best result for just over 35 years, since Konrad Bartelski came second in a downhill in Italy in 1981.
The 30-year-old had finished sixth and seventh already this season.
He told BBC Sport: "The first run was just insane. I knew I had skied it clean, but couldn't believe it when I crossed the finish line.
"In between runs I tried not to get the heart rate up or get stressed. I was trying to tell myself I wasn't the last one to go but it was tough. It was a mental battle with myself but I won the mental battle.
"Hirscher skied so well, so coming second almost felt like a victory. It's crazy. I'm just really proud of what I've achieved."
The Lancastrian races without UK Sport funding after it was withdrawn from the alpine programme in 2010 but does receive other sponsorship.
Ryding, who learnt to ski on a dry slope at Pendle Ski Club, has been a member of the British ski team since 2006 and competed in the 2010 and 2014 Winter Olympics, finishing 17th.
He had a 0.29 seconds lead over Italy's Stefano Gross going into the second run with Hirscher 1.02 seconds behind. But the Austrian, who won the race in 2013 and has won the overall slalom title three times, had a storming second run to move from seventh to first, with Ryding ending up 0.76 seconds adrift.
More than 60,000 spectators were watching and Ryding said the noise was deafening.
"Kitzbuhel is like the FA Cup final in England. The downhill race is the number one but the slalom is also massive. The fans are incredible."
The alpine ski World Cup was formed in 1967 and, in 50 years of racing, Ryding and Bartelski are the only British men to finish on the podium while Gina Hathorn (1967) and Divina Galica (1968) scored top three finishes on the women's circuit.
When Bartelski did it in Val Gardena, Italy, it led a French commentator to say: "This is not possible, he is English!"
In the pre-World Cup era, Britain's Gordon Cleaver won the combined race on the Kitzbuhel's Hahnenkamm course in 1931.
While the alpine team are no longer funded by UK Sport, the Great British freestyle ski and snowboard team are.
Following Jenny Jones' historic slopestyle bronze in Sochi, they will receive £4.9m for the four-year cycle leading to the 2018 Winter Olympics in Pyeongchang, South Korea.
They have had numerous World Cup successes with Katie Ormerod becoming the first snowboarder to win a World Cup big air, while cousin Jamie Nicholls has won in slopestyle, Lesley McKenna and Rowan Cheshire in halfpipe and Zoe Gillings-Brier in snowboardcross.
Skier James Woods has won three World Cup slopestyle events.
Meanwhile in cross-country skiing, Briton Andrew Musgrave recorded his best World Cup result, when he came sixth in a 15km race in Sweden on Saturday.

The report, by Wales' Children's Commissioner Sally Holland, found homes provide the right care for some, helping them feel more stable.
But it also highlighted concerns, such as children being criminalised by frequent police call-outs.
Thirty-four looked-after children were interviewed, along with professionals.
Ms Holland called on people who work with children in care to listen to their opinions and experiences.
"They are the experts on what works and it is important that their voices are heard," she said.
Skier Dave Ryding matched Britain's best ever alpine World Cup result when he finished second in the Kitzbuhel slalom in Austria.
[NEXT_CONCEPT]
Children leaving residential care at 18 feel they lack support while others claim they have limited say in where they will live, a report has found.