The striker only had surgery last month to repair a small meniscus tear in his knee.
But having missed the 3-1 defeat to Costa Rica, Suarez was at his talismanic best when giving Uruguay hope of qualifying from Group D.
The South American side now face Italy in their final game in the knowledge a draw could be enough to seal their progression.
"This is incredible. I had told my team-mates that I had a dream that I was going to score two goals in this match,” he told Univision.
"We had to win this match and we did it playing like Uruguay does in these kind of games. Now we have to think about Italy, another very important rival.
"This victory is for all those people who said so many bad things about the team, it's for them."