The Italian club - who have seen numerous matches postponed due to insufficient funding - have been sold twice already this season, with players and staff not being paid in months.
The former UEFA Cup winners feared they may have had to pull out of the league due to their debts - estimated at a value of 100 million euros - but after the vote the Italian Football Federation (FIGC) have agreed to give the club a loan of five million euros to cover their outgoings until May.
"The resolution was adopted confirming the willingness of the league to help Parma continue in the championship," said Serie A president Maurizio Beretta in a statement.
"If the club is passed over to a bankruptcy administrator on March 19, we shall intervene. We'll decide how exactly to intervene along with the administrator."
He added that Italian football federation president Carlo Tavecchio would travel to Parma to put the proposed plan to the players.
Sixteen out of the 20 clubs in Serie A voted in favour of Parma being granted the emergency funding to keep them playing until the end of May.
Cesena, sitting one place above Parma, were the only club in the league to vote against with three clubs abstaining from voting at all.
In the past, Parma have won several major trophies including three Italian cups, one Italian Super Cup, two UEFA Cups, one European Super Cup and one Cup Winners’ Cup. They also finished as Serie A runners-up on two occasions.
However the club do not currently have enough funding to even provide hot showers for the players post match.
Additionally, players of the club have spoken out saying that they will pay for their own transport to and from games if necessary.
Parma captain Alessandro Lucarelli said: "If there isn't a bus to go to Genoa we'll get five or six cars together and travel in them. We're prepared to pay for the trip ourselves."
The measure means last-place Parma should be able to play Atlanta on Sunday, after its previous two matches were postponed indefinitely because the club could not pay for basic services such as security and electricity.
A hearing to discuss the clubs bankruptcy and its future will take place on March 19.