Former West Ham defender Repka - who had talked up using rough treatment in the pre-match build-up - took just two minutes to make his presence felt with a clattering challenge on Robin van Persie.
The 33-year-old was also involved in a hefty tackle with Fabregas, out of which he came off worst and eventually had to be replaced 10 minutes before half-time.
Fabregas was jeered by the partisan crowd at the AXA Stadium from then on, but had the last laugh when he slotted home following good work by full-back Gael Clichy, before Alexander Hleb added a second after a quick break in stoppage-time.
"It was a bit of a battle," said Fabregas. "Sometimes in the game, you get this kind of thing. Sometimes when you cannot play because they are going in very strong, you have to go for a physical game as well."
Fabregas insisted: "Nobody has a bad intention. I just thought I could get the ball.
"It is true, maybe I was a bit late. He did the same before, this is football, sometimes it happens to you. Of course, I am sorry for him."
Fabregas revealed Repka had "insulted" him before the defender hobbled off with a leg injury late in the first half.
"He started insulting me and I said 'okay, well do not'," said the Arsenal midfielder, who denied he mocked Repka as the Sparta player was forced out of the game.
"He was saying Czech words which I do not understand. Maybe Tomas [Rosicky] can translate for me.
Fabregas added: "But I never play football like this, just to kick somebody.
"You just play because you enjoy it. You want to win for your team.
"I think it is not good for football to say before the game that you will kick players, because after we will be ready for it."