Kreider sped past Austrian captain Gerhard Unterluggauer to convert the Americans' first goal of the tournament 14:42 into the game. Blake Wheeler added a goal 2:33 later, scoring into an empty net with an angled shot after Derek Stepan's quick pass caught Austria's goalie flat-footed.
"It was the way we wanted to start," said Stepan, who had two assists. "We wanted to make sure that we play hard, play a solid game for 60 minutes."
Stepan is coming off a rookie NHL season in which he scored 21 goals for the New York Rangers.
"I hope I can find a way to find the net," he said. "We have a good team, we're confident we just have to keep playing and take it game by game."
Austria got on the board with Marco Pewal's shot over goalie Al Montoya
's shoulder, but Yan Stastny restored the two-goal advantage later in the second period.
It was an emotional return for Stastny to the homeland of his father, NHL legend Peter Stastny, who was watching the game at Steel Arena.
"It is a very special event for me," Stastny said in Slovak. "Every day here is great for me and my family.
"It was a goal for the team. Our line did what we could. We put them under pressure, it was fine, though I think we still can play better."
Kevin Shattenkirk and Craig Smith closed out the U.S. scoring in the third.
The young American team outshot Austria 32-13 on the second day of the tournament that ends May 15.
"They had a very good game. We made too many mistakes and they capitalized on them," Austrian coach Bill Gilligan said.
The U.S. next plays Norway in Group C on Monday.
Notes: In Bratislava, Finland beat Denmark 5-1 in Group D to avenge an embarrassing 4-1 loss to the Danes in the group stage of last year's worlds in their opening game.
Jarkko Immonen, Juhamatti Aaltonen, Antii Philstrom each scored before Denmark answered with one from Nichlas Hardt in the third period. Janne Niskala and Tuomo Ruutu sealed the win later in the third.
Defending champion Czech Republic plays Latvia in another Group D game in Bratislava later Saturday, while Sweden faces Norway in Group C in Kosice.