The Swedes' efforts ultimately gave 5-2 against Vancouver.
Backlund's 2-1, which came just over a minute after teammate Johnny Gaudreau's equalizer, was important.
That gave Calgary respite in the initially close game.
When Elias Lindholm with only two seconds left of the middle period could score 3-1, that team gave another boost and when Vancoucer pressed in the third period, Rasmus Andersson had no problem putting the final result in an empty net.
The Swedes cheered for the victory, but not as loud as Semjon Varlamov, the New York Islanders goalkeeper who has had a taste start to the NHL season.
The Russian cage keeper kept a clean sheet in the premiere against local rival Rangers, stood over the team's second match and when he was back between the posts it became a new zero.
This time, the Islanders won 1-0 over Boston.
- It is the best result I have ever had after two matches, I have never before kept a clean sheet twice in a row in a season opener, Varlamov says according to nhl.com.
Jean-Gabriel Pageau's goal at the start of the third period was enough for victory for the Islanders.
However, two Swedish goals were not enough for Nashville.
Filip Forsberg and Viktor Arvidsson both scored goals at home against Carolina.
But the away team won 4-2 and Nashville went on the first loss of the season.