Suarez helped inspired Barca to fight-back from 2-0 down to win 4-2 in San Sebastian.
Alba enthused afterwards: "He is the best No9 in the world, he's fighting like nobody else, scoring goals and playing to keep his teammates on top."
The result sees Barca go 19 points clear of Real Madrid.
Alba added: "If we were 19 points away from Madrid, they would kill us here. Here we are more critical, the press and the fans. There they cover it more."