In the NHL, confidence is everything. Nothing bolsters confidence more than putting a goal on the board to take a lead over an opponent. It can change the way the scoring team plays. It can affect the way a trailing team plays.
Look at the Predators, one of the most successful teams this season. They have 30 wins in their first 52 games. All but seven of those victories came in games in which the Predators scored the first goal. On the other end of the spectrum, the Kings have 26 losses in 50 games, with 22 of them coming in games when their opponents scored first.