Real Madrid grabbed the spotlight with a five-goal demolition of Valencia, but they remain seven points adrift of neighbours Atletico who beat Levante 2-0 earlier in the day.
Adrian Lopez opened the scoring in the 32nd minute by firing into an empty net after an excellent run and cross by teenager Javier Manquillo, who was making his league debut in place of the injured Juanfran.
Koke then ended the game as a contest with a stunning strike from outside the box on the hour mark, but the hosts' joy was tempered by the sight of Falcao limping off with what looked like a hamstring injury that could keep him out for a number of weeks.
The win moves them to within eight points of Barcelona, who suffered a shock 3-2 defeat to Real Sociedad on Saturday.
Madrid took out their frustrations on Valencia with a stunning first-half display powering them to a 5-0 win at the Mestalla.
Gonzalo Higuain opened the scoring early on and then Cristiano Ronaldo and Angel Di Maria helped themselves to braces during a devastating 11-minute spell just before half-time as Madrid, who beat the same opponents in the Copa del Rey in midweek, ran amok.
Valencia battled back after the break and had a number of chances to pull a goal back but Madrid's defence, with Iker Casillas selected ahead of Antonio Adan in goal, held firm to complete a great night for Jose Mourinho's men, who moved back to within 15 points of Barca.
Osasuna lifted themselves off the bottom of the league table with a crucial 2-1 win over relegation rivals Deportivo La Coruna, who replaced them as the lowest-ranked side.
Kike Sola put the hosts ahead on 28 minutes and Nino doubled the lead 15 minutes into the second half, leaving an impotent Deportivo with too much to do in the remaining half an hour.
The Galicians were second best for most of the game but came into life in the final 20 minutes, and a goal by Javier Camunas in the first minute of stoppage time made for a tense finish. However, Jose Luis Mendilibar's side held on for the three points.
Goals from Javi Guerra and Oscar Gonzalez either side of the break saw Valladolid defeat Real Zaragoza 2-0 in a game marred by both injuries and heavy rain.
Three players limped from the field in a scrappy game in which both sides struggled to create chances in difficult conditions.
On Saturday, Real Sociedad hit back from two goals down to end Barcelona's unbeaten La Liga record in stunning fashion with a 3-2 win at the Anoeta.
All looked to be going to plan for Tito Vilanova's visitors when Lionel Messi and Pedro Rodriguez put them 2-0 up within 25 minutes.
But Gonzalo Castro's brilliant strike gave Sociedad hope before half-time and then, after Barca had lost centre-back Gerard Pique to a red card, Castro's curling effort was deflected into his own net by Barca substitute Javier Mascherano.
That sent the home fans wild, but it got even better in stoppage time when Imanol Agirretxe poked Carlos Martinez's cross from the right past Victor Valdes to clinch a dramatic 3-2 win.
Barca had headed to San Sebastian having dropped only two points in La Liga this season - in October's 2-2 Clasico draw with Real Madrid at the Nou Camp.
Sevilla failed to get Unai Emery's league reign off to the perfect start as an error from goalkeeper Andres Palop gifted Getafe a 1-1 draw at the Alfonso Perez Coliseum.
Jose Antonio Reyes put Sevilla in front with a neat finish shortly before half-time, but the lead lasted only three minutes as Palop got caught under Adrian Colunga's inswinging cross and allowed the ball to float over his head and into the net.
The late game also finished 1-1, with Malaga missing the chance to climb to fourth place as lowly Celta Vigo battled hard for a deserved point at La Rosaleda.
Martin Demichelis bundled the ball over the line after a goalmouth scramble to give the hosts the lead seven minutes before the interval, but Celta grew as the match wore on and levelled 14 minutes from time through Augusto Fernandez.
Granada secured only their second home win of the season as a Jordi Amat own goal and a late strike on his full debut from Recio handed them a much-needed 2-0 triumph over an under-strength Rayo Vallecano.
The action got under way on Friday night as Real Mallorca beat Espanyol 3-2.
Sunday's La Liga Results
Saturday's La Liga Results
Friday's La Liga Result