Gonchar scored on the power play with 2:30 remaining in regulation in Ottawa's 3-2 victory over Washington on Tuesday.
Zibanejad and Condra assisted on O'Brien's goal with 1:23 left in the second period to cut a 2-0 deficit in half and breathe life into the Senators 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, 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."
"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."
Gonchar's winner came after Erik Karlsson wove through the Capitals' defense on a man advantage before finding his partner, who fired a one-timer that deflected of Hendricks in front and past Neuvirth with Ottawa's Chris Neil screening on the play.
Then with time winding down and Washington pressing for the tie, Anderson made a great save on Alex Ovechkin before robbing Mike Ribeiro from in tight.
"My job is just to make sure it doesn't get to three," Anderson said.
The Senators 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 the first period.
A turnover by Guillaume Latendresse midway through the period at the Senators' blue-line allowed Wojtek Wolski to jump on the puck and feed Brouwer, who caught Anderson moving the wrong way.
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.