The hosts looked lively from the onset and they managed to carve out a couple chances inside 10 minutes, although Joaquin Correa failed to capatilise on both occasions.
Wojciech Szczesny came to Juve's rescue after 27 minutes as he produced a fine save to keep out Luis Alberto's long range after Emre Can carelessly lost possession.
Szczesny was proving to be the difference as the Polish international produced a stunning save from point-blank range to keep out Marco Parolo's strike.
The visitors then suffered a blow five minutes before the break when defender Leonardo Bonucci was forced off with an injury and replaced by Giorgio Chiellini.
Lazio's dominance eventually paid off in the 65th minute when Bastos' flick-on deflected in off Can for the own goal.
The home supporters were then silenced after 73 minutes when substitute Joao Cancelo fired home from six-yards out after Paulo Dybala's initial effort was saved.
The turnaround was complete for the Old Lady in the 86th minute when Cristiano Ronaldo converted a penalty after Cancelo had been brought down inside the box.
Juve were able to run down the clock to hold on for victory, which sees them move 11 points clear of Napoli, who failed to win on Saturday evening.