The title holders had missed a penalty in a scrappy first half with Parma goalkeeper Antonio Mirante denying Arturo Vidal.
But after struggling to settle in for 45 minutes, Juve - with head coach Antonio Conte banned for 10 months pending his appeal against match-fixing charges - came to life early in the second.
Lichtsteiner converted a cross from man-of-the-match Kwadwo Asamoah on 54 minutes before Pirlo's free-kick was ruled by the assistant referee as over the line despite Mirante's save.
Parma would go on to control the closing stages with some impressive attacking play, but the home side stood firm to begin 2012-13 with three points.
The Gialloblu were the more dangerous and confident side in the early stages, with Jonathan Biabiany making himself known in the final third on more than one occasion and Marco Parolo putting a free header from a corner over the bar after 13 minutes.
Pirlo, Juve's primary source of creativity, was left to feel the effects of a number of clattering challenges but the strategy of keeping Juve quiet by keeping Pirlo quiet was working until around the half-hour mark when the champions were able to begin to threaten.
The Parma back line dealt with a number of advances until the 32nd minute when Lichsteiner moved into the area from the right and found himself brought down by Mirante, earning the keeper a yellow card even though replays proved that the Swiss wide man should have been stopped by an offside flag in the build-up.
Nonetheless, Mirante found redemption by keeping out Vidal's poor effort from 12 yards and the visitors went into the break with parity.
A half-time change of tactical approach worked wonders for the Old Lady and they began the second half in much better stead, utilising the flanks to a greater degree with Lichtsteiner and Asamoah causing all sorts of problems.
The two would combine for the opener less than 10 minutes into the half as Asamoah effortlessly strugged off Gabriel Paletta before firing in a driven cross for Lichtsteiner to finish.
Parma continued to target Pirlo, and a few minutes after going behind Alessandro Lucarelli was booked for clattering the midfield maestro with a forearm to the face.
Pirlo would have the last laugh, however, firing a dipping free-kick from just outside the box at Mirante, with the assistant referee who made the penalty decision in Juve's favour deeming that the keeper had not done enough to keep it the right side of the goal line.
Biabiany and Massimo Gobbi tested Marco Storari in search of a route back into the match, before Ishak Belfodil came on in place of Dorian Pabon and spearheaded a late charge by Parma.
He and Jamie Valdes created a number of additional chances as the away side pushed to get off the mark for the season at the very least, while Sebastian Giovinco - signed from Parma in the summer - almost added a third for Juve on two occasions only to be denied by the offside flag and the side netting.
Sotiris Ninis came off the bench and put Storari to work once more with a decent pair of speculative distance drives, but the title holders began their defence with three points and a clean sheet even without their manager.