Ben Maxwell scored in the second period for Montreal, which beat Florida 3-2 on Thursday in its preseason opener.
Milan Michalek scored in his debut for Ottawa (0-3).
"The biggest thing is trying to get out there and feel comfortable," said Gionta, who played on a line with Tomas Plekanec and Max Pacioretty. "There are so many new guys, guys that I've never played with, it's just a matter of time to feel comfortable. The first period was a little slow, but I thought the second and third period our line really had some good chances, some good jump, and it felt pretty good."
Senators No. 1 goalie Pascal Leclaire stopped 16 of 17 shots in two periods, while Robin Lehner made 12 saves in the third.
"They're unbelievable players," said Michalek, who was acquired along with Jonathon Cheechoo from San Jose on Saturday in a trade for Dany Heatley. "We had good chances but we had some breakdowns in the defensive zone and we have to get better there."
Maxwell, who was stopped by Leclaire on a breakaway late in the first, drew the Canadiens even with a power-play goal 15:15 into the second.
Montreal's Eric Neilson got three fighting majors in the game and had a game misconduct added to his last bout with Ottawa's Cody Bass, who was also ejected following their fight midway through the third.