In-form Real Madrid reclaimed second spot from Barcelona, thanks to a crushing 3-0 win over struggling Villarreal, while Valencia climbed above Sevilla into fourth after Jordi Alba struck an 82nd-minute winner in a 1-0 victory at Real Zaragoza.
Six straight wins had lifted unbeaten Levante, whose annual budget of around 20 million euros ($27.6 million) is one of the smallest in the league, above Barca and Real to the top of the standings for the first time in the 102-year history of the tiny Valencia-based club. Their latest success, the first time any club other than Barca and Real have won seven in a row since 2002, gives them 23 points from nine matches, one more than Real and two ahead of Barca following the champions' 1-0 win at Granada on Tuesday.
Daniel Estrada put San Sebastian-based Sociedad ahead in the fourth minute at Levante's Ciutat de Valencia stadium.
Nano levelled for the home side nine minutes after the break with a deflected shot and Valdo nodded Levante in front seven minutes later before Inigo Martinez drove the ball through a crowd of players for an 86th-minute equaliser.
Suarez smashed in a superb long-range free-kick deep into second-half added time to ensure Levante can live the dream for a few more days at least.
Defeat for Villarreal heaped more pressure on their coach Juan Carlos Garrido, whose side are 17th with only seven points and are on the verge of elimination from the Champions League.
Karim Benzema starred for Real, netting a sixth-minute opener and sending Angel Di Maria clear for the home side's third just after the half hour. Brazilian playmaker Kaka scored the second with a fine strike from just outside the penalty area in the 11th minute.
In other games, 10-man Malaga lost 2-0 at Rayo Vallecano and stay sixth, Getafe drew 2-2 at home to Osasuna and Real Mallorca lost 1-2 to visiting Sporting Gijon.
