Olofsson's power-play goal from the right face-off circle made it 1-0 at 6:27 of the second period.
"It's obviously fun to have some kind of record, even if I want to get that 5-on-5 goal as well," said Olofsson, who has played 11 NHL games. "It felt a lot better today, my overall game, and I'm sure it will come soon."
Dallas forward Andrew Cogliano said, "As a team, that's when you have to really bear down and get a kill, and it's on the guys on the ice. We've been a decent penalty-kill team all year (78.6 percent). Would like to have that one back because I think if we would've killed it we would've been in much better shape in terms of trying to win the game."
Reinhart made it 2-0 with 2:04 remaining in the second with a one-timer from the high slot off a pass from Olofsson.
"We didn't let up after we had the lead," Johansson said. "We kept going and we kept playing the right way, didn't really force things as we've done a little bit in previous games. We made it hard for them, and it was 60 good minutes."
Skinner finished a 3-on-1 off a pass from Vladimir Sobotka to make it 3-0 at 4:20 of the third period.
Johansson made it 4-0 with a one-timer from the point at 6:02.
The Stars went 0-for-2 on the power play and are 1-for-22 (4.5 percent) this season.