Meanwhile, the defending champion Viktoria Rebensburg of Germany took bronze, a further 0.20 seconds off the pace.
In tricky weather conditions that tested the athletes’ technique and nerve, the 30-year-old Slovenian clocked a combined total of 2min 38.87 seconds over the two runs in Rosa Khutor.
Maze, who had shared the downhill title with Switzerland's Dominique Gisin in the first week, after the first ever dead heat in an Alpine race at the game, looked as if she was not in the mood for sharing again, setting a blistering pace with the quickest time in the first run.
That meant the Slovene started last of the top 30 racers in running order for the second descent, and had to look on anxiously as her main rivals attacked her time.
Leading the challenge was Fenninger, who was herself looking for a second gold after winning the super-G. Fourth after the first run, the Austrian then stormed into the lead, which changed hands no less than seven times in a dramatic final run.
By the time Maze launched herself out of the gate, the tension was palpable. Starting with an 0.85 second lead over the Austrian, the Slovene’s deficit was slowly eroded, but she hung on through to the finish line to sneak home by just seven-hundredths of a second.
“I can live with that!” said a delighted Maze. “This season I'd focused on the Olympics. I was ready for this, it's what I came here to do.”
“It was tough for me to keep the same rhythm as last year in the World Cup, but I knew I was going to show my best here, it's great. The rest of the season doesn't matter.”
It has been a remarkable Winter Games for Maze. Last year's overall World Cup winner and a triple-medallist at the Schladming world championships, Maze had been left stunned with her poor performances at the start of the season.
However, Sochi 2014 has seen her produce a terrific return to form, which, she says, vindicates her decision to appoint a new coach Mauro Pini, just a month before the Games.
“You don't normally change coaches in mid-season," she acknowledged. “But I had that opportunity, so why not if it could work out better for me?”
Despite missing out on gold by such a slender margin, Fenninger was also pleased with her performance.
“My second run was really cool,” said the 24-year-old. “After the first run I knew in the start I would have to take a lot of risk and I did and I'm really happy that that was enough for a medal.”
Meanwhile, the 2010 gold medallist Rebensburg was delighted to make the podium again after an indifferent first run left her well down the field.
“I can hardly believe it,” she said. “I was quite far down in the first run but I knew I could go looking for a bit more. I'm still not firing on all cylinders but I got a medal and that's essential.”
Rebensburg laid down the fastest second run, but other frontrunners faded, with Sweden's World Cup giant slalom leader Jessica Lindell-Vikarby and American teenager Mikaela Shiffrin falling out of contention.
Shiffrin ended up fifth at 0.50 seconds, just behind Italy’s Nadia Fanchini (+0.38 seconds), and must now refocus her bid to become the youngest American to win an Olympic Alpine gold on the slalom.
Super combined winner Maria Höfl-Riesch was a late withdrawal after complaining of flu symptoms.