The veteran defenceman scored on the power play with 2:30 remaining in regulation in Ottawa's 3-2 victory over the Washington Capitals.
Trailing 2-0, Zibanejad and Condra assisted on O'Brien's goal with 1:23 left in the period to cut the deficit in half and breathe life into the team heading to the third.
"I thought they were the best line and the best guys play," Senators coach Paul MacLean said. "They were the best group by far so we had to make sure we got them on the ice."
Zibanejad, who was recalled from the American Hockey League on Monday morning, was named the game's first star. When asked if he had earned the right to play Wednesday night against the Montreal Canadiens, MacLean quipped: "We usually play the first star."
Zibanejad, who has battled injuries this season with the Binghamton Senators, showed his skill and speed in his first NHL action since the beginning of the 2011-12 campaign.
"I was hoping I would play good," he said. "I was nervous in the first period, but then I got that out of the way and started playing like I should and felt pretty good."
The Senators should consider themselves lucky to walk away with the two points after showing little emotion through most of the first two periods.
"This was huge," Ottawa captain Daniel Alfredsson said. "I think we know from last year that we've got to play to the end. We were in tough and they played really well. They forechecked us really hard and we really couldn't get a handle on the puck and create any offence."
In comparison, the Capitals could only shake their heads at the lost opportunity. After losing their first four of the season, they arrived in Ottawa high on their first win and hopeful to start a streak.
"I thought we played good," Neuvirth said. "It's very disappointing to not even get a point."
Gonchar's winner came after Erik Karlsson wove into the Capitals' zone on a man advantage before finding his defence partner, who fired a one-timer that deflected off Hendricks in front and past Neuvirth with Ottawa's Chris Neil screening on the play.
"My job is just to make sure it doesn't get to three," said Anderson.
After O'Brien, who celebrated his 24th birthday, scored late in the second, the Senators then quickly tied the game at 2:20 of the third. Kyle Turris won a faceoff in the offensive zone and pushed the puck ahead to Michalek, who scooped it passed a surprised Neuvirth.
"It happened very quick," Neuvirth said. "They won the faceoff and he just hit it. I'm not even really sure. I need to see the video."
Playing without Jason Spezza because of an undisclosed upper-body injury, the Senators struggled and the Capitals owned much of the momentum in the first period, jumping out to a 2-0 lead.
Washington then made it 2-0 as Hendricks tipped Jay Beagle's shot home.
The Senators continued to struggle in the second and seemed incapable of breaking through the Capitals' forecheck as Washington pinned the home side in its own end for nearly two minutes, leading to a chorus of boos from the 19,267 on hand at Scotiabank Place.
"It's a tough one because when you play a really good hockey game you obviously want the win," Capitals coach Adam Oates said. "When you have a 2-0 lead it should be enough in this league."
Notes: LW Kaspars Daugavins and D Andre Benoit were healthy scratches for the Senators. Apart from Spezza, D Jared Cowen (hip, out for season), D Mike Lundin (finger, two weeks) also missed out due to injuries. ... C Brooks Laich (strained groin, out indefinitely), D Jack Hillen (upper body, out indefinitely) sat for Washington with injuries, while C Marcus Johansson, D Tom Poti and D Roman Hamrlik were healthy scratches.