Gibson made 31 saves for Anaheim, which had won seven in a row and was 18-2-2 in its final 22 regular-season home games.
"They played how you're supposed to play in the playoffs," Cogliano said. "They played patient and played the right way. When you get chances, you have to score on them."
Kane made it 2-0 at 13:51. Pavelski skated into the zone on a 2-on-1 off a stretch pass from Brenden Dillon before passing to Kane, who cut across the crease and scored on a backhand.
Kane said he wasn't nervous in his playoff debut.
"I thought I got better as I went along," he said.
Burns gathered a loose puck at the right point and beat Gibson five-hole through a screen to make it 3-0 at 15:15.
"We were OK in the first period," Getzlaf said. "We didn't really come out flat, but we didn't execute with the puck at a high enough level in the first period. In the second period, we were chasing the game a little bit and resulted in us taking too many penalties."
San Jose outshot Anaheim 8-4 in the first period and 17-9 in the second. Burns hit the post from the high slot 4:01 into the game, and the Sharks went on their first power play at 4:57 when rookie defenseman Marcus Pettersson was called for holding Timo Meier, the first of seven minor penalties against the Ducks.
"Way too many penalties," defenseman Francois Beauchemin said. "When we had success down the stretch (of the regular season), we didn't take as many. One or two a game. That's it. It was uncharacteristic for our team."
The Sharks were 1-for-6 on the power play. The Ducks went 0-for-3.
