Ivan Pelizzoli performed numerous saves until Mirko Vucinic broke through with a late brace.
"It had seemed to be a cursed game," said Conte. "We were shooting from all angles, getting the goalkeeper or the woodwork. Pelizzoli had a fantastic game.
"Pescara also scored an incredible goal with Emmanuel Cascione, as perhaps we should've been a bit calmer after that. We were a little nervous that we'd ruin it all the same way we did against Sampdoria.
"This was not an easy victory, but I am happy with the performance and relieved because these are three fundamental points."