Handanovic's reputation as a penalty expert has continued to rise since arriving at Inter in 2012, and he saved a spot-kick for the second straight game on Saturday.
The Slovenian kept out Maxi Lopez in last week's 4-0 win over Sampdoria and he repeated the trick at Parma, tipping Antonio Cassano's penalty onto the post on the stroke of half-time at Stadio Ennio Tardini.
Gabriel Paletta was sent off for a second yellow card in the first minute of the second half and Hernanes' free-kick that followed was headed in by Rolando in the 48th minute.
The defender nodded home unmarked and the goal will have done his hopes of sealing a permanent switch from Porto no harm after voicing his wish for a transfer in the game's build-up.
Substitute Fredy Guarin wrapped up the points with a late long-range stunner as Inter moved five points clear of the Parma in the race for UEFA Europa League qualification.
Cassano, returning from an ankle injury, was tenacious in front of the onlooking Italy boss Cesare Prandelli, forcing a superb save from Handanovic before shooting wide with his left foot after Cristian Molinaro had surged down the left wing.
Inter gradually worked themselves into the game and Mauro Icardi should have opened the scoring, only to put his free header into the side netting after Hernanes' corner.
Rodrigo Palacio then had a fierce volley tipped over by Parma goalkeeper Antonio Mirante and he continued to impress, keeping out a 20-yard effort from Esteban Cambiasso.
The flashpoint of the first half would come with just three minutes left, as a heavy first touch saw Walter Samuel, already booked in the sixth minute, bring down Marco Parolo in the penalty area.
Handanovic was Inter's hero again though, tipping Cassano's penalty onto the post, and Raffaele Palladino could only turn the rebound wide.
And there was still time for Inter to be denied by the woodwork as well, as Cambiasso, following up a blocked shot, struck a wicked left-foot effort from outside the area that hit the inside of the post and then Mirante's legs, leaving the veteran perplexed as the ball snuck out for a corner.
Parma's hopes suffered a blow when Paletta received his second yellow card for a lunge on Palacio in the 46th minute, and Inter took the lead from the resulting free-kick.
Slack marking from the Parma defence allowed Rolando, free at the back post, the simple task of heading Hernanes' ball back across the face of goal and in.
The woodwork would again keep out both sides, with Hernanes hitting the outside of the post with a free-kick before Parma's Alessandro Lucarelli – who powerfully rose above Samuel and Rolando – saw his header thud into the bar.
Parma kept pressing, as Parolo volleyed over, but Inter's numerical advantage would eventually make a difference, as Guarin lashed a 25-yard strike into the bottom-left corner in the 89th minute to extend his side's unbeaten run to five.
