Baggio, who scored all 11 penalties he took in the league last season, stepped up for the 72nd-minute spot-kick after Ronaldo had been brought down by Fabio Cannavaro. The former Italian captain, famed for his penalty miss at the end of the 1994 World Cup final against Brazil, hit his shot low and hard but wide of Gianluigi Buffon's right-hand post.
"I did it to please the public," joked Baggio after the match. "Seriously though, I just hit it as I would any other penalty but unfortunately it was too far wide."
Parma had taken the lead through Diego Fuser, who curled a sweetly struck free-kick inside Gianluca Pagliuca's near post after 54 minutes.
Both sides squandered chances in an evenly balanced game, but in the end Buffon's agility and Parma's defensive superiority won out. Alberto Malesani's side have conceded just nine league goals all season, while Inter have now let in 21.
Parma's eighth Serie A victory of the season kept them within three points of the leaders, Fiorentina, who beat David Platt's struggling Sampdoria 1-0 thanks to a 27th minute strike by Rui Costa.
Serie A's leading scorer, Gabriel Batistuta, turned provider this week, unleashing Rui Costa down the left wing. The Portuguese midfielder cut inside and slotted a diagonal shot past Fabrizio Ferron.
Sampdoria remain one place above the relegation zone and have the worst defensive record in Serie A after conceding 28 goals.
Christian Vieri scored his first goal for Lazio in his first league appearance in four months with a header 11 minutes from time to give Sven Goran Eriksson's side a 1-0 victory at Bologna which rekindles their title challenge.
In Spain, two second-half goals from Davor Suker led Real Madrid to a 3-1 win over visiting Salamanca and moved them up to third place in the Spanish League. Real could go top on Sunday if they can win at the leaders, Mallorca.
Carlos Casartelli put Salamanca ahead in the first half, but Raul equalised before the interval, heading in after a Clarence Seedorf free-kick had been pushed against the bar by the visiting goalkeeper, Bogdan Stelea.Reuse content