For 90 minutes at the Juventus Stadium it looked like Conte's men would not capitalise on second-placed Napoli's surprise defeat at Chievo, but substitute Emanuele Giaccherini arrived just in time to fire Juve nine points clear at the top of the table.
With 10 games left and no head-to-heads remaining between the title rivals, the Scudetto is Juve's to lose but Conte stressed the importance of taking each game as it comes.
He told juventus.com: "We wanted to win the game at all costs, showing heart and desire right until the death. We faced a well-organised side who put 11 men behind the ball.
"We had our chance, but it became even harder as the game wore on. Having said that, we were always in control and prevented them from hitting us on the counter.
"Today's [Sunday] victory was important but we still haven't won anything. We'll immediately turn our attentions to our next 'final' against Bologna.
"This week - in which we've faced Napoli, Celtic and Catania - has taken it out of us and that's why I gave everyone an unscheduled day off."
Giaccherini emerged from the bench as Conte grew frustrated with misfiring forwards Mirko Vucinic and Sebastian Giovinco and the tactical switch paid dividends, with the midfielder bundling the ball home with seconds to spare.
The 27-year-old said: "I dedicate this goal to myself. I work a great deal during the week to make sure I'm ready to seize these opportunities.
"I don't know if this will turn out to be the goal that decides the Scudetto, I hope so. For the moment, it's important for the team and takes us nine points clear of Napoli."
Catania boss Rolando Maran, however, pulled no punches after being banished from the touchline for overzealously demanding a free-kick for his team in the first half.
Maran then watched from the stands as Giaccherini undid all his side's hard work in stoppage time, and he later told La Repubblica: "I'm sorry we lost like that. It's like a bad joke.
"It's such a shame because we were controlling the game so well.
"I think that for the goal, and at other times before it, there were certain refereeing decisions that put us at a disadvantage.
"But I'm still satisfied with the team's performance and I'm still confident we are on the right track."