Marco Parolo's first-minute opener sealed the points away at 10-man Sassuolo to move Parma within sight of a Europa League place, as fellow chasers Verona stumbled in a scoreless draw at home to Bologna.
Parma's steady climb back up the Serie A table has left them outside the European spots in sixth, but with a game in hand -- after a recent away fixture at Roma was rained off -- Tommaso Ghirardi's side will fancy a late run at seizing a place in Europe.
Juventus remain top of the pile with an eight-point lead on Roma but have the chance to increase their advantage to 11 points with victory away at AC Milan in Sunday's late game.
Napoli, who are seven points behind Roma in third, are away at Livorno while fourth-placed Fiorentina host Lazio later in a bid to pull further clear of Inter, in fifth.
Inter did well to come away with a share of the points from a scoreless draw at Roma on Saturday, however dropping two points has also given a boost to fellow teams chasing a Europa League place.
Parma, helped by Sassuolo striker Domenico Berardi's red on 72 minutes for a foul on Cristian Molinaro, are now on 40 points, only one behind Inter, and sit one place ahead of Verona, who suffered a setback after being held to a scoreless draw by relegation-haunted Bologna, who after missing an earlier penalty were reduced to 10 men when Jonathan Cristaldo saw red on 82 minutes.
Coach Roberto Donadoni played down Parma's Europa League qualifying ambitions, but said: "We're now 14 matches unbeaten and we'll try to continue.
"I have to applaud the squad because this is all the fruit of their hard work."
Most of Sunday afternoon's games featured teams with faint hopes of a Europa League place and others battling to stave off the threat of relegation.
Atalanta claimed a 2-1 home win over Chievo with Luca Cigarini scoring an 85th minute winner after Dario Dainelli had levelled Carlos Carmona's first-half opener for the hosts in the 72nd minute.
Chievo were reduced to 10 men on 68 minutes when Bostjan Cesar, who had already been cautioned, saw red for a foul on German Denis.
Luca Antonelli and Stefano Sturaro scored in either half to secure a 2-0 home win for Genoa against relegation-haunted Catania, who were reduced to 10 men before the interval after Giuseppe Bellusci saw red for a second bookable offence.
Gian Piero Gasperini's men are now 11th and being chased by Sampdoria, who continued their resurgence under coach Sinisa Mihajlovic with a precious 2-0 away win at Torino to pull themselves up to 12th.
"Now we can say we're safe from relegation," said Gasperini. "We'll be playing in Serie A next season, and that's not to be laughed at."
Stefano Okaka made the most of a rare start for Samp to score a seventh-minute opener as confusion reigned in the Torino box, with Manolo Gabbiadini sealing the points on 79 minutes.
Okaka said his maiden goal of the campaign was down to a change in attitude: "A lot of things have happened this year, a lot of them down to me, and I lost my way a little," said the 24-year-old Italian.
"I needed to mature but now I'm more sure of my football and am playing much more relaxed."
Earlier, Udinese got reacquainted with defeat in a 3-0 reverse at Cagliari which dropped Francesco Guidolin's side back towards the drop zone.
A series of missed chances, notably by veteran striker Antonio Di Natale, before and after Victor Ibarbo's 18th minute opener, proved costly.
Matias Vecino and Agim Ibraimi added further goals in the space of seven second-half minutes to pull Cagliari eight points clear of the danger zone.