Levante struck early and relied on its staunch defence when reduced to 10 men to beat Osasuna 2-0 at home in the Spanish league on Saturday.
Levante's win extended its unbeaten streak to eight consecutive rounds and provisionally lifted it ahead of Sevilla and Valencia into seventh place.
First-year coach Joaquin Caparros had set the goal of avoiding relegation for Levante this season, but after 26 rounds the Mediterranean minnow is closer to earning a Europa League berth than worrying about the drop.
"My team is a pain to play against," said Caparros. "With 10 players we tripled our effort and [goalkeeper Keylor] Navas, with the way he is playing, kept us calm at the back.
"We can play better or worse, but this team always gives it its all. It's all soul."
Midfielder Papakouly Diop gave Levante the lead at Ciutat de Valencia Stadium just four minutes in when his long-range strike bounced past goalkeeper Andres Fernandez and inside the far post.
Forward Ruben Garcia doubled the hosts' advantage by fending off Damia Abella to control a long free kick before turning and firing the ball home.
Levante played the last half hour with 10 men after Victor Casadesus saw a direct red card for a hard tackle from behind on Alvaro Cejudo, but even though Osasuna finally mustered its first shot on goal it never threatened to come back.
"It's disheartening to play against Levante when they are ahead in the score," Osasuna coach Javi Gracia said.
Levante visits league leader Real Madrid in the next round.
Elsewhere, Elche beat Celta Vigo 1-0 thanks to a late goal by Carles Gil, Malaga drew 1-1 at home with Valladolid, and Getafe was held to 0-0 by visiting Espanyol.
Elche's Manuel del Moral and Eduardo Albacar both sent the ball off the goalframe in the first half before Rafina tilted the match in Celta's favour through his skilful dribbling and passing.
But Gil combined with Ferran "Coro" Corominas to break free in the box and net the winner six minutes from time to give Elche its first victory in four rounds and move the promoted side six points from the drop.
Valladolid's draw at Malaga left it in the relegation zone, three points behind Malaga and Almeria.
Malaga's Roque Santa Cruz was left unmarked to head in the 13th-minute opener, but Valladolid dominated the rest of the match after Javi Guerra went close in the 20th.
Midfielder Daniel Larsson equalized 10 minutes later after Manucho knocked down a long cross by Antonio Rukavina for the Swede to score.
"Our fans are nervous and I understand them," said Malaga coach Bernd Schuster, whose team has one victory in its last nine games.
"We got the first goal, which is very important, but then we had the wrong attitude and take a breather [instead] of looking for a second."
Getafe's drab draw with Espanyol meant its winless streak grew to 11 straight games dating to November. It also lost goalkeeper Miguel Moya to a leg injury in the second half. Espanyol stayed in 10th place.
Madrid leads Atletico Madrid and Barcelona by three points. Madrid visits Atletico on Sunday, when Barcelona hosts Almeria. Also, Real Sociedad plays at Sevilla, Villarreal hosts Real Betis, and Valencia visits Rayo Vallecano.
Athletic Bilbao routed Granada 4-0 on Friday to hold onto fourth place and the final Champions League spot.