Three days after a last-gasp 2-1 win over Zenit in the UEFA Europa League, Sevilla appeared laborious and were far from their best, as Diego Mainz proved decisive at both ends of the pitch.
The Granada centre-back put the hosts ahead in the 16th minute and Sevilla failed to find a way back into the contest until the 69th minute.
Again Mainz was involved, turning Aleix Vidal's low cross past his own goalkeeper for his third own-goal of the season, inspiring something of an onslaught from Sevilla towards the end.
But, with Kevin Gameiro's inexplicable miss from two yards in stoppage time, Sevilla were forced to settle for a point, failing to fully capitalise on Valencia's defeat to Barcelona on Saturday, while Granada remain second-from-bottom.
Villarreal's dismal run in the league stretched to six games without a win as Marcelino's men somehow failed to find the net in a 0-0 draw with rock-bottom Cordoba.
The hosts had 28 shots in total, the highest number they have managed in a single match this term, but they could not make the most of their absolute dominance and slumped to an underwhelming stalemate.
In the day's early kick-off, Rayo Vallecano beat Almeria 2-0 to move on to 41 points, effectively securing their status as a top-flight club for another year, with Miku scoring his first goal for the club right at the end.
And a Nolito penalty five minutes before half-time earned Celta Vigo a 1-0 win at Eibar, who remain just three points above Almeria and the drop zone.
