Italy defender Bonucci smashed home almost identical spot-kicks in each half at the Stadio Olimpico in Rome to move Juve sixth, level on 21 points with fifth-placed Lazio.
Massimiliano Allegri's side are now four points from the Champions League positions, with Atalanta occupying fourth following their 5-2 thumping of Spezia earlier on Saturday.
It was a dogged, solid away performance typical of Allegri's best sides and a good sign ahead of Tuesday's trip to Stamford Bridge to face Premier League leaders Chelsea.
"It was a really important win, it's always hard to play matches after the international break but we know that with this approach and spirit of sacrifice that results depend on us," said Bonucci after his first Serie A double.