They leapt even further into the spotlight, right off the bat, by introducing "Jeopardy!" host Alex Trebek to announce their first choice.
The draft -- similar to the NFL -- is being held remotely at team sites across two days, with league executives stationed at the NHL Network in Secaucus, New Jersey. From his television setup there, commissioner Gary Bettman welcomed Trebek, a graduate of the University of Ottawa, into the broadcast as a "special guest."
Trebek, standing at his traditional "Jeopardy!" dais, took it from there and announced "The NHL" as the topic. He eventually announced the selection of German center Tim Stutzle with the third overall pick, as the "Jeopardy!" theme music played in the background.
It was an unexpected moment for a nondescript franchise that traditionally doesn't make many headlines. But Trebek, 80, currently battling stage 4 pancreatic cancer and a recipient of the Order of Canada, performed a key moment for the team with his traditional, stoic delivery that "Jeopardy" viewers have been familiar with since 1984.
At No. 5, the Senators selected Jake Sanderson, the first American player to be drafted this year. A defenseman out of the University of North Dakota, he is the son of former NHL forward Geoff Sanderson. The second pick was announced by Ottawa general manager Pierre Dorion, who thanked Trebek for the first selection. At No. 28, Ottawa closed its night by selecting Canadian center Ridly Greig.
In a rare draft oddity, the Senators joined the New Jersey Devils as two franchises with three first-round picks on the same night. New Jersey opened its run, at No. 7, selecting Swedish forward Alexander Holtz, and chose Canadian center Dawson Mercer at No. 18, followed by Russian defenseman Shakir Mukhamadullin at No. 20.
Also in the first round, the Winnipeg Jets selected No. 10 overall. A key number in their franchise history -- 10 was the number worn Hall of Fame forward Dale Hawerchuk, who died in August from stomach cancer -- the Jets introduced Hawerchuk's wife, Crystal, to make the pick.
After thanking the hockey community for its well wishes to the family, Hawerchuk announced the Jets' choice of Canadian forward Cole Perfetti.
"Our family would like to thank the Winnipeg Jets and all of Dale's loyal fans and friends for their love and support," she said. "I want you to know that he loved Winnipeg and always felt a special connection to the people of Manitoba. We both consider Winnipeg our home."
The draft, originally scheduled to be held in Montreal, began with the New York Rangers selecting the consensus No. 1 prospect, Canadian forward Alexis Lafreniere. From suburban Montreal, Lafreniere was the first Canadian to go No. 1 since Connor McDavid was chosen by Edmonton in 2015.
With the final pick of the first round, San Jose Sharks assistant general manager Doug Wilson, Jr. ended with a sweet touch. Wilson used American Sign Language to spell "Ozzy" as he announced the team's selection: Ozzy Weisblatt, a winger from Calgary. Weisblatt was raised by a single mom, who is deaf. Weisblatt learned ASL before he could talk and uses it regularly to communicate with his family at home.
The Weisblatt family was shown during the broadcast, screaming and jumping up and down in celebration in their living room.
Bettman began the broadcast with an announcement that the league is planning to begin next season on Jan. 1, 2021. Rounds 2-7 of the draft will be held Wednesday.
Information from ESPN's Emily Kaplan was used in this report.