Bilbao, who spent the first half of the season toiling around the relegation zone but have surged up the standings since Gaizka Garitano took charge in December, strolled into a first-half lead with Yuri Berchiche's fifth minute strike and an own goal by Aitor.
But they lost control of the game after the interval and Levante pulled a goal back through striker Roger Marti's penalty, while Uruguayan defender Erick Cabaco headed in an equaliser in the 89th.
Bilbao reacted by pouring down the other end and earning a penalty when captain Iker Muniain collided with Levante's Moses Simon, prompting furious protests from the visiting side, who had had a goal ruled out in the first half.
Spain international Muniain smashed the ball high into the net from the spot, giving his side a third consecutive league victory which leaves them eighth in the standings, four points behind fourth-placed Getafe after 30 games.
Celta had come from two goals down to beat Villarreal 3-2 last weekend but looked set to do the opposite against Huesca.
They went 2-0 up with goals either side of halftime from Spain international Brais Mendez and Iago Aspas but Huesca scored three times in the space of 10 minutes to lead 3-2.
Algeria international Ryad Boudebouz levelled in the 81st minute for Celta, who are 18th in the standings but trail 17th-placed Villarreal by one point.
Rayo took the lead in coach Paco Jemez's second game in charge but second-half goals from Charles and Pedro Leon saw Eibar turn the game around.
Huesca are bottom on 23 points, Rayo are 19th with 24.
(Reporting by Richard Martin, editing by Pritha Sarkar)
