The home side looked set for another disappointing day until the veteran popped up in the 81st minute with the only goal as Inter ended a run of three consecutive defeats to move them up to fifth in the Serie A standings ahead of today's later matches.
Stramaccioni's men came into the game nine points shy of the last Champions League place while a midweek Coppa Italia semi-final defeat to Roma ended their last chance to win silverware this season.
Furthermore, plans to salvage a consolatory Europa League place were dealt a further blow as midfielders Esteban Cambiasso and Fredy Guarin joined an injury list which already included Antonio Cassano, Diego Milito, Joel Obi, Gaby Mudingayi, Luca Castellazzi, Cristian Chivu, Dejan Stankovic, Ibrahim M'Baye and Walter Gargano.
Parma, meanwhile, were without suspended defender Gabriel Paletta, with Jonathan Biabiany, McDonald Mariga, Raffaelle Palladino, Emilio MacEachen and Fabiano Santacroce all nursing injuries.
They came into the contest off the back of a demoralising 3-0 home defeat to Udinese and it was Inter who started the game strongly.
The hosts should have taken the lead after 17 minutes when Parma failed to clear a set piece, however, from just eight yards out and with just Antonio Mirante to beat, Matias Schelotto shot straight at the goalkeeper.
After 28 minutes Nicola Sansone drifted past Andrea Ranocchia, but with just Samir Handanovic to beat he, like Schelotto, failed to test the opposition stopper.
Moments later the Inter keeper had to tip a Marco Parolo effort over before Jaime Valdes crashed an effort onto the bar when the resulting corner broke to the edge of the area.
Parma were firmly on the front foot and after the Inter back-line failed to close down Marco Marchionni, the winger elected to shoot with his effort just falling wide of the post.
Parma's passage of dominance seemed to wake up the hosts and the visitors were thankful for Yohan Benalouane's last-ditch block to deflect Schelotto's effort wide with the winger just eight yards out and with the goal at his mercy.
The second half failed to be as fast-paced as the end of the first and it took until the 63rd minute for the next meaningful shot on goal when Rocchi fired wide from the edge of the box.
Parma hit back and great forward play from Amauri set Sansone free and - with few options on - he fired just wide from 20 yards out.
Handanovic was called into action after 75 minutes with his face deflecting substitute Jonathan Biabiany's effort away from danger.
With nine minutes left, finally the breakthrough came for Inter as Mateo Kovacic played in Jonathan down the right and his pullback found Rocchi.
The veteran mishit his shot but with Mirante already committed the ball went into the net.
The relief around the San Siro was palpable as the home side held out for what could be a vital victory.