"I don't consider any win easy but we came out and played the game we wanted to play, and I think we didn't make the game easy for them," Tavares said.
The Islanders have won three straight against the Penguins dating back to last season, their longest winning streak in the series in more than five years.
Two of those victories have come on the road, something New York hadn't done in Pittsburgh since 2002.
While the Islanders aren't getting too far ahead of themselves just six games into the season, the way they dominated a team considered a Stanley Cup favorite is a welcome confidence boost following a late collapse in a loss to Winnipeg on Sunday.
"I'm sure nobody gave us much of a chance against a really good hockey team, but you know what I thought systematically we were a little more structured, over the last game for sure," coach Jack Capuano said. "We were a little more sound in a lot of areas tonight."
Pascal Dupuis scored with just more than a minute remaining to avoid the shutout but it wasn't nearly enough to keep the Penguins from losing for the third time in their past four games.
Marc-Andre Fleury stopped 13 shots before being pulled after the second period. Fleury and backup Tomas Vokoun received little help from Pittsburgh's defense. The Penguins gave it away 11 times, with two of the turnovers leading to New York goals.
"I'm not sure if we're pressing early, and then it doesn't happen and you get away from things," Pittsburgh center Sidney Crosby said. "As you see tonight, we get a couple bad bounces, ended up down early and seems like we let that frustration kind of get to us."
The Penguins had scored first in each of their five games this season, but Cizikas gave the Islanders a well-earned early lead by stealing the puck from Paul Martin deep in Pittsburgh's zone, then swooping behind the net and wrapping it around an outstretched Fleury.
The goal served as an exclamation point on a period the Islanders dominated in a place where they rarely win. New York went in a loser in 13 of its previous 14 visits to Pittsburgh, the victory a 5-3 triumph last March that derailed any hopes the Penguins had of catching the New York Rangers for the Atlantic Division title.
Pittsburgh expects to be in the mix again during this truncated 48-game season but has hit an early rough patch that left the largest crowd in the brief history of Consol Energy Center voicing its displeasure following another disjointed effort.
The Penguins were drummed 5-2 by Toronto in the home opener last Wednesday and appeared no sharper six days later against another young, quick team that flustered Pittsburgh with its forechecking.
"We want to be a team that plays with pace and (is) tough to play against, and make teams come out of their own end and play a full 200-foot game," Tavares said. "When we're skating and getting on the forecheck, that's when we're most successful and that's what we've been doing, and I think that was evident tonight."
Not that the Penguins needed any help giving it away.
The Islanders went up 2-0 at 6:46 of the second period when Pittsburgh defenseman Deryk Engelland misplayed a New York clearing attempt at the blue line.
The puck bounced off Engelland's stick and the speedy Grabner pounced, beating two Penguins up the ice, then flicking a wrist shot that deflected off Fleury's glove and into the net.
The goal seemed to briefly energize Pittsburgh, which spent the next five minutes buzzing Nabokov. All the pressure failed to produce a goal, and a pair of power-play tallies by the Islanders late in the period put New York firmly in control.
Tavares wristed a pretty cross-ice pass from Moulson by Fleury to make it 3-0, and Moulson scored less than two minutes later, collecting a long shot off the end boards and stuffing it by a foundering Fleury.
The goaltender actually fell on his rear after the initial shot and failed to get up before Moulson stuffed it by him, a fitting ending to a maddening night.
Nabokov had no such problems. He improved to 10-2 lifetime against Pittsburgh, which went 0-for-3 on the power play, including a fruitless 5 minutes spanning the second and third periods after New York's Colin McDonald was hit with a boarding penalty and a game misconduct for his hit on Penguins defenseman Ben Lovejoy.
"We definitely deflated ourselves with the power play," Pittsburgh's James Neal said. "But we've just got to have a better effort all over the ice, 5-on-5 and we just didn't have it tonight."
Islanders F Jesse Joensuu is out five to seven weeks after having sports hernia surgery. Joensuu sustained the injury while playing in Europe during the NHL lockout ... Pittsburgh D Matt Niskanen is day to day with a right foot injury ... The Penguins announced earlier Tuesday that Consol Energy Center will host the second USA Hockey All-American Prospects game Sept. 26, 2013. ... The Islanders play at New Jersey on Thursday while the Penguins play in New York against the Rangers.