Peterson was mobbed by his teammates moments later.
"It was fun," Peterson said with a smile after the game. "I didn't expect to score in the first period, but I'm feeling good. It was fun to score."
Over the past 10 seasons, Peterson became the fifth Stars player to score a goal in his first career NHL game - the first since Jason Dickinson on April 7, 2016 vs. Colorado. He's also the sixth Stars player to score his first career NHL goal on his first shot over the past 10 seasons, joining Denis Gurianov (Nov. 10, 2018 vs. Nashville), Dickinson (April 7, 2016 vs. Colorado), Mattias Janmark (Oct. 8, 2015 vs. Pittsburgh), Brett Ritchie (Dec. 31, 2014 vs. Arizona) and Antoine Roussel (Feb. 1, 2013 vs. Arizona).
Peterson skated on a line with Roope Hintz and Joe Pavelski, and finished the game with a goal and a plus-1 rating in 16:35 TOI.
"I grew up watching these guys, and now I get to play with them," Peterson said of his Stars teammates. "It's a dream come true. I really enjoyed my first game. A fun and great experience to play here."
The Stars seemed to be in full control when Radek Faksa got on the board with a power-play tally at the 6:11 mark of the second period, but it wasn't long after when the Rangers began their push.