The 20-year-old Haaland scored a 54th minute penalty, awarded for a foul on Reyna, and bagged another with a sensationally quick counter-attack and a Jadon Sancho assist as Dortmund utilised their fearsome youthful attacking weapons.
Norway forward Haaland, who joined in January, took his tally to 15 goals in his 16 Bundesliga games so far this year.
A day after Bayern Munich opened their season with an 8-0 demolition of Schalke 04, Dortmund sent a warning to the title holders with their dominant performance over Gladbach, who will be competing in the Champions League this season.
Reyna opened the scoring, after combining perfectly with his fellow 17-year-old Jude Bellingham in the 35th minute. His first league goal made him Reyna the second youngest American to score in the league after Christian Pulisic.
Gladbach had a good early chance through Jonas Hofmann but struggled throughout with Dortmund's speed, and not even the introduction of strikers Alassane Plea and Marcus Thuram could turn things around.
The hosts, playing in front of a crowd limited to 9,300 fans in their 80,000-capacity stadium due to COVID-19 restrictions, also hit the crossbar with a Sancho header.
"It was a really good start to the season. We have a lot of young guys and a great balance with older guys too. Really exciting game," Reyna said after the match. "It's great to have fans back. To score and help the team makes it even better. Yeah, it was a great start."