Jacobo Ramón opened the scoring in the 23rd minute, converting from close range after a driving run and cross from Nico Paz, before Kaiki Bruno da Silva added a second in the 83rd minute following a goalmouth scramble. David Romero pulled one back for Parma in stoppage time, but it proved only a consolation as Como moved level with Lazio on 10 points.
Fàbregas made five changes from the side that beat RB Leipzig in the Champions League in midweek, handing full debuts to summer signings Moise Kean and Kaiki alongside goalkeeper Robert Sánchez, and admitted the timing of the win mattered as much as the result.
"It wasn't about fear of drawing instead of winning, it was about the importance of the goal," Fàbregas said. "After a performance like that, when you take 31 shots and score only once... they can cause you problems.
"This was a hugely important match for us, and for me as a coach maybe even more so, to see what happens inside their heads, even after the Champions League win. To see who can handle it and who can't. If we hadn't put in those first 45 minutes today, we would have risked losing. I liked it, without it being perfect, but it isn't a cheap win - it was worked for and important."
Fàbregas was also pleased with the impact of his substitutions, having made five changes during the match.
"If you don't see games out with low energy, you'll lose points, I'm convinced of that," he said. "The team responded well with the five changes, I liked the players who came on, and it was important for me to understand the message my players gave me. I trust them more for it, and there can be more rotation in the future - that has to happen if we want to win certain matches."
For Parma, head coach Carlos Cuesta struck a note of regret despite the defeat, pointing to missed chances that could have earned his side a point.
"We're left without points, which is what we wanted to avoid," Cuesta said. "There are positive signs: I think we played well in the first five or 10 minutes. Then they dominated and we couldn't get past the halfway line. We finished the first half well, and in the second half we had several chances that could have let us equalise. After the 2-0 we managed to score and kept pushing, it's a shame we didn't make the most of all our opportunities.
"Now we'll analyse it and improve for the game against Genoa."