La Liga leaders Atletico Madrid won 2-1 over Osasuna, although they had gone behind in the 75th minute after Ante Budimir’s strike.
The goal also came shortly after second-placed Real Madrid had gone 1-0 ahead at Athletic Bilbao, meaning as it stood, Los Blancos were top of the table.
But Atleti hit back with Renan Lodi levelling in the 82nd minute before Suarez scored a dramatic 88th minute winner.
“He is always there,” Atletico boss Diego Simeone said about Suarez.
“He gives us leadership and who better than him to solve a game that we could have lost without him.”
The result means that Atletico holds their two-point buffer from Real heading into the final day. Atletico are away to relegation battlers Valladolid while Real host seventh-placed Villarreal.
“We will prepare with the same enthusiasm for the final day as we have done since I arrive in 2011,” Simeone said.
“The team will be fierce and I want the fans to continue to feel proud of what we have done.”
Meanwhile, Real boss Zinedine Zidane said: “We’re still in the title fight and we’re going to give our all until the final minute. I’m happy with our performance, a very good game, we’re still alive and we’re going to fight until the end. We knew it was going to be this way.”
He added: “It’s been very difficult but we’re still in the fight. Real Madrid have lost two league titles on the last day and we’re going to try to win this one in the last minute. We’re going to give our all to win this league title.”