Barcelona and Real Madrid both won on Saturday, meaning the title could be decided next weekend.
Cesc Fabregas' 84th-minute strike earned a below-par Barcelona a narrow victory over Levante at the Camp Nou as they remained 13-points clear at the summit.
David Villa had seen a 16th-minute penalty saved by Keylor Navas, and that looked like it would prove a costly miss as Barca - perhaps with one eye on Tuesday's Champions League semi-final first leg against Bayern Munich - struggled to break down a spirited Levante defence, before Fabregas' late breakthrough.
The win means Tito Vilanova's side, 13 points clear of second-placed Madrid, could win the title next weekend, despite Real's 3-1 win over Real Betis earlier in the evening.
Mesut Ozil scored twice to ensure Real Madrid will go into their Champions League semi-final clash with Borussia Dortmund on the back of a Primera Division win.
Germany international Ozil broke the deadlock against Real Betis on the stroke of half-time and then wrapped up the scoring with his second right at the end.
In between those two strikes, Karim Benzema had put Madrid 2-0 up before Betis pulled a goal back through Jorge Molina's 73rd-minute penalty.
Granada are a point clear of the relegation zone after coming from behind to draw at home with Real Valladolid.
Patrick Ebert gave the visitors a surprise lead in the second half with a gloriously struck free-kick but Youssef El-Arabi levelled with 18 minutes remaining.
The hosts were the better side throughout the 90 minutes and pushed for a late winner but were unable to beat the outstanding Valladolid goalkeeper Jaime Jimenez.