Peluso, signed from Atalanta earlier this month, outjumped his marker and headed Serie A leaders Juventus in front in the 63rd minute following Emmanuele Giaccherini's cross from the left.
Lazio, third in Serie A, levelled four minutes from time when Stefano Mauri scored from close range after Antonio Candreva's corner was headed back into the area.
Juventus, who as usual rested goalkeeper Gianluigi Buffon and Andrea Pirlo from the competition, struggled in the first half and survived several letoffs.
They nearly went ahead nine minutes after the re-start when Alesandro Matri's first-time volley was tipped over by Federico Marchetti.
After going in front, Juventus threatened to get a second as Arturo Vidal hit the post when he should have scored and also had a header saved by Marchetti.