Conte's side were made to work hard for their victory against a Parma team who had gone 17 league games without suffering defeat.
A quickfire first-half double from Carlos Tevez put the hosts in command, before Parma pulled a goal back in spectacular fashion with a volley from former Juve defender Cristian Molinaro.
Amauri was then sent-off for Parma following an elbow on Giorgio Chiellini as the Serie A leaders held on to restore their 14-point advantage at the top.
The win marked a Serie A record 15th straight home league win for Juve, a feat achieved despite injuries to the likes of Angelo Ogbonna, Andrea Barzagli and Federico Peluso.
And Conte, who has had to contend with a schedule that has been congested by their participation in the UEFA Europa League, was full of praise for his players.
"This was a wonderful important victory against a team that was unbeaten in 17 rounds and they showed their strength again," Conte told Sky Sport Italia.
"You don't put up a run like that if you don't have quality. Let's not forget we are in an emergency situation, so I have run out of words to praise these lads for playing every three days with no space for squad rotation.
"I am well aware they are pushing all the way and some need to rest, but at the moment we can't afford to do that.
"So far the campaign has been extraordinary, but as I always say records aren't worth much if you don't get something tangible at the end of it.
"These players deserve a trophy, as often they even surprise me."
