Levante climbed to fourth in La Liga after claiming a 2-1 win at Espanyol.
The Madrid-outfit travelled to Barcelona and claimed a crucial win which takes them back into the top-four.
Valdo gave Levante the lead midway through the first-half, but substitute Kalu Uche looked to have rescued a point for home side.
But in added time, Levante's own sub Suarez was the hero as his free-kick deflected into the corner of the net.
Top-four seeking Malaga came from behind to hammer bottom-of-the-table Real Zaragoza 5-1, and move fifth in the table.
Aranda put Zaragoza ahead midway through the first-half, but Malaga levelled just before the break through Sebastian Fernandez.
Malaga did not take the lead until 23-minutes from time when Paulo da Silva put through his net. This opened the floodgates as Martin Demichelis, Isco and Salomon Rondon added to the scoring.
Real Betis and Getafe remain clear of relegation trouble after playing out a 1-1 draw in Seville.
Betis had taken the lead just after the interval through Jorge Molina, but a Dorda own goal just moments later meant Getafe took a share of the spoils.
At the bottom, Racing Santander and Sporting Gijon remain in the bottom-three after they drew 1-1.
David Barral gave Sporting the lead just before the break, but Racing rescued a point with 16-minutes left as Cristian Stuani scored from the spot.