The Socceroo goalkeeper's Spanish club gained a shock comeback win in round 36 action at sixth-placed Celta Vigo after twice trailing on Tuesday (Wednesday AEST).
That moved Levante up three places to 16th in the extraordinarily tight relegation fight.
Ryan pulled off a stunning double save, like he has done numerous times during the campaign, in first-half added time to deny Hugo Alvarez.
The 34-year-old also kept out an 84th-minute Borja Iglesias shot to secure all three valuable points.
With Elche subsequently losing 2-1 at Real Betis there are five teams, including Levante, on 39 points. Last of those are Girona, in the relegation spot of 18th, with Alaves one point and one place below.
Sevilla, meanwhile, are on 40 points and above them are plenty more clubs that are simultaneously fighting to avoid the drop and to win a place in Europe: Getafe, in seventh, are six points clear of Girona.
Trailing to a fourth-minute goal by Alvarez, Levante went into halftime level through Jeremy Toljan two minutes from the break.
Javi Rueda restored Celta's lead soon after play resumed but Levante levelled again, Honduran Kervin Arriaga scoring in the 57th minute.
Six minutes later Jon Ander Olasagasti gave the visitors an improbable lead in Galicia and Ryan held Celta at bay to snatch the three points.
Ryan, 34, joined Levante, the 11th European club of his nomadic career, in August and has established himself as the No.1.
The Valencia club have a home game against 15th-placed Mallorca and away trip to Real Betis to complete their season.
Elsewhere, fourth-placed Atletico Madrid won 2-1 at mid-table Osasuna.
Manuel Pellegrini's Betis meantime, sealed fifth and are back in the Champions League after a 20-year absence.
9°C