Benoit and Dziurzynski scored their first NHL goals and Craig Anderson made 37 saves and the Ottawa Senators defeated the New York Islanders 3-1 on Tuesday.
"I've played a few years to get here so to finally score a goal in the NHL is special," Benoit said. "Since I was a young boy I've been thinking about this."
Travis Hamonic scored for the Islanders, who got 23 saves from Rick DiPietro in his third start of the season.
Benoit's goal at 8:37 of the second period made it 2-0 for Ottawa and came a little more than two weeks after he thought he originally had his first on Feb. 3 in Montreal. But a goaltender interference penalty that day on Jakob Silfverberg negated the goal.
On Tuesday, Silfverberg made a nice pass to Benoit for a one-timer past DiPietro.
"The first one would have never went in if (Silfverberg) wasn't standing there so I can't blame that on him. Tonight it was a great pass and he made a good play," said the 29-year-old Benoit, who played in his 21st NHL game after five years in the American Hockey League and three other seasons in Europe.
"It was disappointing for that first one not to count, but I knew eventually that it would come. It doesn't matter when it comes it's just nice to have it."
Hamonic's wrist shot at 2:44 of the third period cut the Ottawa lead to 2-1 and ended a scoreless streak of 103:19 for the Islanders.
Dziurzynski, in his third professional season, gave the Senators a 3-1 advantage at 17:25 of the third with his first goal in just his third NHL game.
DiPietro couldn't handle the left winger's initial shot and Dziurzynski poked the rebound home.
Senators rookie defenseman Eric Gryba picked up an assist for his first NHL point.
"It's an outstanding feeling. Since I was a little kid I've always wanted to play in the NHL and I'm very happy that I got here and that I got to do it early when I've only played three games," said the 23-year-old Dziurzynski.
"I'm just happy he got his and I got mine on the same night. We've been playing well defensively we've just had some trouble scoring goals. It's good to get a couple on the board and hopefully get some confidence and get some offense rolling."
Greening opened the scoring in the second period for a struggling Ottawa power play that came in on an 0-for-24 slump.
With five Islanders, including DiPietro, around him, Greening jammed in a loose puck home for his second of the season at 6:01.
Benoit then added his goal from Silfverberg just 2:36 later.
The Islanders put on the pressure, but Anderson held off New York until Harmonic scored early in the third.
Islanders coach Jack Capuano said his team played a good game, especially after a 7-0 home loss to the Philadelphia Flyers on Monday.
"It's a loss but (the) guys obviously worked hard. We had a lot of chances, we stayed the course and kept to the game plan but their goaltender played well," Capuano said. "We had a good system review (Tuesday) morning. Obviously our game wasn't very good against Philadelphia and we just wanted to go out and work hard for one another and play with a lot of passion. I thought we did that. We did a lot of good things."
Notes: The Senators were 1 for 5 on the power play, while the Islanders went 0 for 4. ... Chris Neil reached 1,900 penalty minutes for his career, all with the Senators, in Monday's win at New Jersey ... Islanders defenseman Matt Carkner missed his homecoming Tuesday as he sat out the game with a groin injury. Carkner, a native of Winchester, just outside Ottawa, spent three seasons with the Senators before signing with the Islanders in the offseason. ... Matt Moulson has played in 262 consecutive games, which is the fourth-longest streak in Islanders' history.