* Subdued Barca beat Levante 1-0
* Injuries mar Real's 3-1 win over Betis
* Valencia thrash Malaga 5-1 (Updates with Valencia win, adds quote)
MADRID, April 20 (Reuters) - Midfielder Cesc Fabregas moved Barcelona a step closer to the La Liga title with a late strike in a laboured 1-0 victory at home to mid-table Levante on Saturday.
The 84th-minute goal secured a win that took Barca to 84 points with six games left, 13 clear of champions Real Madrid who earlier beat Real Betis 3-1 with a Mesut Ozil double.
A victory away to Athletic Bilbao next Saturday, and a Real defeat at city rivals Atletico Madrid would enable Barca to be crowned champions for a fourth time in five years.
In the late game, Valencia's push for a top-four finish was boosted with a 5-1 thrashing of Malaga at home when they scored four times in six first-half minutes.
Valencia climbed to fifth with 53 points, pushing Malaga down to sixth on 50, and they are one point behind fourth-placed Real Sociedad, who visit Osasuna on Sunday.
Betis are seventh with 48 points.
The top two fielded weakened sides with next week's Champions League semi-finals in mind.
Barca visit Bayern Munich for their first leg on Tuesday, and Real travel to Borussia Dortmund on Wednesday.
Barcelona lined up with four fullbacks in defence, Eric Abidal making his first start in over a year since having a liver transplant and playing the full 90 minutes.
The French international partnered Adriano Correia in the centre of defence, while usual first-choice players such as Xavi, Sergio Busquets and Jordi Alba started on the bench.
World Player of the Year Lionel Messi failed to make the squad as he recovers from a hamstring strain.
Barca had an early chance to take the lead when Andres Iniesta tumbled to win a dubious penalty but David Villa's 17th-minute spot kick was saved by Levante keeper Keylor Navas.
The Costa Rican went on to pull off a string of saves against a Barcelona side lacking spark and a sense of urgency.
Barca substitute Alexis Sanchez help break the deadlock six minutes from time, crossing from the right for Fabregas, who controlled the ball and fired low into the corner in a crowded area.
"Obviously it is difficult to think about any game other than the one against Bayern. It will be one of the games of the year," Spain international Fabregas told reporters.
"But it is good to be able to go into it with a win behind us."
In Madrid, Real were without regulars such as Xabi Alonso, Sergio Ramos and Sami Khedira and after a scrappy opening period were forced into an early change when Marcelo went down injured.
The Brazilian left back was carried off on a stretcher with a muscle injury after falling awkwardly.
Betis, chasing a place in Europe next season, had an effort ruled out for offside early on and Dorlan Pabon skimmed the bar.
Cristiano Ronaldo carried Real's greatest attacking threat and soon after he had crashed a 25-metre shot against the upright, a moment of Ozil inspiration broke the deadlock.
The Germany midfielder cut in off the right flank, exchanged passes with Karim Benzema on the edge of the area, and lifted a finish inside the near post just before the break.
A breakaway started by Ozil led to Ronaldo feeding Benzema to net the second in the 57th minute.
Midfielder Luka Modric was substituted with a muscle strain midway through the half and in the 71st minute Real youth-team defender Nacho brought down Ruben Castro for a penalty.
Jorge Molina scored from the spot and Betis almost snatched a late equaliser when Castro hit the bar and Raul Albiol cleared the follow-up off the line.
However, Real went straight down the other end and Ozil turned Jose Callejon's deflected shot into the net from close range to seal the points.
Valencia left Malaga reeling as they scored four times in six minutes, starting when midfielder Dani Parejo dribbled through the centre of the visiting defence to net in the 25th minute.
Spain striker Roberto Soldado fired in at the back post three minutes later and he grabbed his second from the penalty spot in the 30th.
Sergio Canales tapped in the fourth after Willy Caballero could only parry a Jonas shot on a counter-attack in the 31st.
Julio Baptista's free kick over the wall gave Malaga a glimmer of hope just before the break but Ever Banega made it 5-1 with a fierce shot that was too strong for Caballero in the 56th.
Relegation-threatened Granada recovered to draw 1-1 at home to mid-table Real Valladolid, with Youssef El-Arabi's header cancelling out Patrick Ebert's superb free kick. They are one place and one point above the drop zone. (Reporting by Mark Elkington; Editing by Sonia Oxley and Ken Ferris)