Robbie Keane, on loan from Spurs, also got on the scoresheet for the first time with a penalty while Morten Rasmussen doubled his Hoops' tally since arriving from Brondby last month with a second-half strike.
Celtic, with eight new faces in their squad following a busy January transfer window, face a crucial run of four league games as they attempt to claw back Rangers' 10-point lead.
They host Hearts at Parkhead on Wednesday before travelling to Aberdeen on Saturday. Dundee United are then next up at home before the Old Firm derby at Ibrox on February 28.
Kamara believes Celtic's reshuffled squad are about to click into gear at just the right time.
"The important thing now is to try to build on that kind of display," he told The Evening Times.
"We are a team that has not played very often together and there are a lot of new faces.
"But I think once we get two or three games together that you will see a very good side because there are some fantastic players here.
"We know how important the game against Hearts is, but for the confidence I think it was good for the team to win against Dunfermline and I think we now want to take the same kind of form into the game against Hearts.
"Everyone knows that we need to start winning games in the league."
Kamara was delighted to open his account, adding: "When you are a striker it is always important for your confidence to come in and get a quick goal at a new club because it helps you to settle.
"I was pleased with the way I played and the way the team performed.
"It was a good afternoon. I feel good and that I am settling into the side, so I want to keep my place and keep playing."