The Austrian, who has now won six of the seven slaloms this season, also moved atop the overall standings.
"My slalom season has really been perfect," Schild said.
Schild skied the Neveros course in a two-run combined time of 1 minute, 43.61 seconds.
Tanja Poutiainen of Finland was second, 0.32 seconds behind, and Veronika Zuzulova of Slovakia third, 0.93 back.
Resi Stiegler of the United States, who stood second after the opening run, did not finish her second trip down, losing control after posting a fast split time.
"I saw Resi before me did not finish and I thought maybe not to attack full," said Schild, who also led after the first run.
Schild lost some of her lead midway through her second run, but held on in the steep lower section and clinched victory with the 10th fastest second leg.
The only slalom races Schild did not win this season came in the World Cup in Semmering, Austria, in December, and the world championships in Are, Sweden, earlier this month. Schild won the silver medal at the worlds behind Czech skier Sarka Zahrobska.
"A gold in slalom would have been great but Sarka was faster," Schild said. "But now I have the slalom title and also a chance at the overall."
Schild has 660 points to top the slalom standings. Ana Jelusic of Croatia, who finished fifth Sunday, is next, 332 points behind. Wins are worth 100 points each, so Schild has an insurmountable lead.
Zahrobska finished sixth in her first race as world champion.
Last season, Schild finished second in the slalom standings behind Janica Kostelic, who is taking this year off.
If Schild wins the final two slaloms _ in Zwiesel, Germany, on March 11 and in Lenzerheide, Switzerland, on March 17 _ she can match Kostelic's record of eight slalom victories in 2000-01. Kostelic won all eight in succession, however.
In the overall standings, Schild moved back ahead of teammate Renate Goetschl, who did not enter the slalom. Schild leads with 1,052 points, Goetschl has 1,019, Nicole Hosp of Austria moved into third with 989 and Julia Mancuso of the United States dropped to fourth with 959.
Hosp finished fourth Sunday with the fastest second leg and Mancuso was 15th.
Olympic champion Anja Paerson missed a gate early in her first run and did not finish. Michaela Kirchgasser, who won Saturday's giant slalom, also skied out in the opening leg.