Ligety held on to his first-run lead and finished in an aggregate time of 2 minutes, 30.80 seconds to beat Raich by just 0.18. The 36-year-old Austrian trailed by 1.61 after the opening run before posting the fastest second-run time and making up almost 1 ½ seconds on the American.
Henrik Kristoffersen of Norway was 0.25 behind in third for his first career GS podium, four days after winning the junior world title in GS.
In spring-like conditions on the Podkoren course, Ligety didn't take too many risks in his final run and saw his comfortable lead shrank at every split time.
"I am not the kind of person that tries to cut off lines so I just tried to ski smart and be clean as much as I could," said Ligety, who earned his fourth GS win of the season and 21st overall. He also won a super-combined event in Switzerland in January.
The victory also puts Ligety back in contention for the World Cup title in the discipline. He reduced his deficit to leader Marcel Hirscher, who came fourth, to 50 points with one race remaining and each victory worth 100 points.
"At this point the giant slalom globe isn't a huge goal of mine," Ligety said. "I have to win and he has to falter which is not a really good strategy. If it was anybody else besides Marcel I would say it's doable, but Marcel is not the kind of guy that gives anybody any gifts."
Raich returned to a World Cup podium for the first time since February 2012, when he won a super-G in Crans Montana, Switzerland. The Austrian was "surprised how close I've come to Ted."
"I am very happy with second place, that's a great result," said the 2007 overall champion, who will decide on his future after the season is over. "I am still having fun and I can still be fast."
The 19-year-old Kristoffersen added another chapter to his fairytale breakthrough season, which includes his first World Cup win in a slalom two months ago and an Olympic bronze medal.
"It's been a really good couple of weeks," Kristoffersen said. "I am really happy about my skiing, that is the most important thing. If I end up 10th and I've skied the two best runs of my life, I have to be happy. If I am on the podium, it's even more exciting."
Kristoffersen said the support of his dad Lars, who also coaches him, helped him. Lars Kristofferson wasn't in Sochi but is accompanying his son for the last two weeks on the World Cup.
"He was standing on the hill. It's for sure great to have my dad here," Henrik Kristoffersen said. "Usually he is watching the TV and I call him before I run. Now it's really nice to have him here for the last two weeks."
Aksel Lund Svindal of Norway finished 17th and remained in the overall lead, 41 points clear of Hirscher. The Austrian can overtake Svindal after Sunday's slalom, which the Norwegian will skip.
"I wish I was faster obviously because that would be the way, especially for my overall chances, to put some pressure on Marcel," Svindal said. "I have to be realistic. Downhill and super-G is where I should do the work."
Hirscher called the race "brutally hard."
"For me those are useful points," the Austrian said. "I have managed to reduce my deficit. It remains tight. If I can win tomorrow, that would be cool, I would have some buffer."
Hirscher is chasing his third straight overall title and would become the first Austrian to achieve the feat. Only Italy's Gustav Thoeni (1971-73), Sweden's Ingemar Stenmark (1976-78) and American Phil Mahre (1981-83) have done it.
Leif Kristian Haugen posted faster intermediate times than Ligety in the opening run but had a nasty crash just before the finish. The Norwegian led Ligety by 0.10 when he lost his balance and fell through the final gate before sliding over the finish line. But as his skis had passed the gate correctly, he avoided disqualification.
Haugen finished the race in 15th, 1.75 behind Ligety.
Americans taste speedskating success
Heather Richardson, of West Jordan, did it again Saturday in Inzell, Germany, claiming her second speedskating World Cup win over 500 meters one day after her first.
Shani Davis won and Brian Hansen finished third in the men's 1,000 as American speedskaters went some way toward easing the disappointment of their Sochi medal shutout.
Davis finished in 1 minute, 8.70 seconds, ahead of Dutchman Stefan Groothuis by one tenth of a second and Hansen by two tenths. Davis increased his lead in the overall standings to an unassailable 470 points.
Richardson won in 37.70 seconds, beating Russia's Olga Fatkulina by 0.14 and Germany's Jenny Wolf by 0.19, to close the gap on overall leader Lee Sang-hwa of South Korea to just 10 points.
Olympic champion Ireen Wust of the Netherlands won the women's 3,000 in 4:01.52, beating Czech skater Martina Sablikova by 2.48 seconds and compatriot Yvonne Nauta by 2.92.
Dutchman Ronald Mulder defeated twin brother Michel, the Olympic champion, in a direct confrontation to win the men's 500 in 34.96, ahead of Canada's Gilmore Junio and Germany's Nico Ihle. Michel Mulder finished fifth.
Another Dutchman, Arjan Stroetinga, won the 20-lap mass start race
Shiffrin retains slalom title
American Mikaela Shiffrin retained her World Cup slalom title on Saturday in Are, Sweden, adding to her Sochi Olympics gold medal in the discipline just five days before her 19th birthday.
Shiffrin led from start to finish, as she did at the Sochi Games two weeks ago. Shiffrin now has Olympic and world championship gold medals and two World Cup titles in her specialty event.
"My first win was just amazing, it was the start of all of this," she said the 2013 slalom title. "It was finally in my mind, I felt like I could be a good ski racer at the World Cup level."
Shiffrin defended her title in a combined two-run time of 1 minute, 50.66 seconds. She finished 0.60 ahead of Swedes Maria Pietilae-Holmner and Anna Swenn-Larsson, who earned her first career podium finish in third.
Shiffrin, of Vail, Colo., earned 100 World Cup points for her fourth victory of the season to clinch the title. She moved 130 ahead of Frida Hansdotter of Sweden, who placed fourth, with one race remaining.
"I'm just really comfortable on slalom skis," Shiffrin said. "It feels so easy to me when I'm just loose and I let my skis go. It seems they find the finish for me, I don't have to work so hard."
In a tight race for the overall World Cup title, Maria Hoefl-Riesch of Germany retook the standings lead from Anna Fenninger of Austria, who doesn't race slalom.
Hoefl-Riesch placed seventh, trailing Shiffrin by 3.26, to earn 36 race points. She moved 29 ahead of Fenninger as she seeks to repeat her 2011 overall title, which she won by three points ahead of American Lindsey Vonn.
Second-run racers coped with steadily falling snow and poor visibility after morning sunshine lit the first-leg course. Shiffrin had the advantage of the second-leg gate-setting being designed by her personal coach on the U.S. team, Roland Pfeifer.
The final four races are scheduled next week at Lenzerheide, Switzerland. Shiffrin's goal is to win a giant slalom race this season.
"I know my giant slalom skiing is fast, fast enough to win," she said. "But I really have to do my best skiing."