Ullmark stopped all 15 shots he faced in the first period before being replaced by backup Carter Hutton to open the second period because of a lower-body injury.
Ullmark was shaken up during an intense Devils scramble in front, which ended with the goalie reaching out to glove Nico Hischier's snap shot from the high slot six minutes in. Ullmark was slow to get up and eventually was tended to by Buffalo's medical staff before being cleared to continue playing.
The Sabres opened the game minus captain Jack Eichel, who was sidelined by what the team is calling a lower-body injury.
Without being specific, Sabres coach Ralph Krueger said Eichel's injury developed during warm-ups and was not related to him missing the morning skate earlier in the day.
"It definitely caught us all by surprise. The first diagnosis on it is day-to-day," Krueger said.
As for Ullmark, the coach said more tests are required to determine the severity of the injury.
Hutton stopped 25 shots in relief of Ullmark.
The Associated Press contributed to this report.