Dan Vladar made 31 saves for Philadelphia, which eliminated Pittsburgh in six games in the Eastern Conference First Round last season.
"I think it was as ugly as it could have gotten," Flyers defenseman Travis Sanheim said.
Robertson made it 1-0 at 7:26 of the first period when he deflected Kris Letang's pass down the right slot past Vladar.
Robertson scored his second at 11:52 of the third period to make it 6-0. His shot on a short-handed rush missed the net but caromed off the end boards and was kicked in by Vladar.
The forward had been acquired from the Toronto Maple Leafs for a fourth-round pick in the 2028 NHL Draft on July 1.
"First game you're kind of nervous, and it's not preseason, you're playing in a tough building on the road," Robertson said. "Obviously, I was fortunate to get the one, and obviously that second one was kind of a gimme. I'll take it. It was a good start for the guys. It's good to feel comfortable."
Robertson played on a line with Crosby and Rickard Rakell, and in the short time they've been together Robertson has already impressed.
"I think he's got great speed and just works every shift," Crosby said. "He brings the same thing and he's got a great shot, so yeah, I think it's more his effort than anything."
Robertson wasn't the only newcomer to impact the score sheet. It was also the first game for the Penguins for Lapierre and defensemen Kaedan Korczak (two assists) and Declan Carlile (one assist).
"I think it just builds confidence," Crosby said. "I don't think it's ever easy for guys to start with new teams, but I think having the benefit of (training) camp and just trying to get on the same page there. There's a number of guys that are with us for their first game, so I think that helps. There's other guys in the same situation, so hopefully we're on the same page as much as we can."
Koivunen made it 2-0 at 15:44 of the first period. Samuel Girard's pass in transition caught the Flyers on a line change, allowing Koivunen to skate in alone and score between Vladar's pads.
Malkin extended the lead to 3-0 at 5:03 of the second period with a power-play goal. He finished a give-and-go with Lapierre with a one-timer from the left circle.