Both sides spurned clear chances in a captivating first half, but the deadlock was eventually broken when Caceres exploited Inter's poor marking to head in Andrea Pirlo's corner.
Juve veteran Del Piero then came off the bench to net the second, latching onto Arturo Vidal's incisive through ball to drill a low effort inside the near post.
Juve had to win to keep the heat on leaders Milan and the Old Lady could have made it three - but Maicon made a superb goal-line clearance from Leonardo Bonucci late on to keep the score respectable.
Claudio Ranieri has always struggled to get the better of Juventus in management, winning just two of his 18 attempts.
But his Inter side created the best chance early on when Maicon cut inside from the right and found Diego Milito, though the Argentine could only poke his shot straight at the advancing Gianluigi Buffon.
Juve hit back with a couple of great chances of their own, but Alessandro Matri's wastefulness in front of goal cost the home side as he planted a free header straight at Julio Cesar.
The first half of this Derby d'Italia was played at a terrific tempo that saw the game ebb and flow, with both sides enjoying their fair share of attacks.
But Juve shaded it and should have led when Caceres drilled a low ball into the feet of Matri, but he snatched at his shot and the ball flew harmlessly over the bar.
Inter could have sneaked ahead when Diego Forlan's glancing header almost caught out Buffon at his near post, but the visitors' best moment came when Milito brought down Dejan Stankovic's long ball with a sublime first touch only to drill his shot straight at the Italian number one.
Inter were made to pay for their poor finishing 12 minutes into the second half when Juve drew first blood.
Finding space in the Inter penalty area, the unmarked Caceres nodded in Pirlo's outswinging corner to give the Old Lady a deserved lead - and left Inter's players blaming each other for leaving the Uruguayan in so much space.
But the game's big moment was reserved for Del Piero, whose perfectly timed run was spotted by Vidal. The veteran striker latched onto the ball and showed there is still plenty left in the tank with a precision finish into the far bottom corner.
The Nerazzurri toiled for a route back into the game but struggled to create chances without Wesley Sneijder, as Forlan and Milito both ended up isolated for long periods.
Juve could have easily added to their lead late on, with Maicon making a superb interception on the line to deny Bonucci before Giorgio Chiellini brought the best out for Julio Cesar with a bullet header that the Brazilian goalkeeper acrobatically tipped over.
Inter will have been relieved when the final whistle sounded, while Juventus will be buoyed by a crucial win that keeps the pressure on leaders Milan with nine games to play.