Ullmark made 34 saves in what became his first win since December 19.
The 31-year-old has had a long and tough road back after a period of injury problems at the end of last year. He has conceded three or more goals in his last five matches.
One of the night's conceded goals was scored by San Jose's Swedish defenseman Timothee Liljegren, when he shot 2-1 in numerical superiority halfway through the second period.
Ullmark played the entire match and is credited with a save percentage of 91.9 percent. San Jose's goalie Vitek Vanecek saved 27 shots, with a save percentage of 87.1 percent.
