Suarez latched onto a cross from Jordi Alba to give Barca the lead in the first leg of the semi-final tie at Camp Nou.
Barcelona are now only the second team in Champions League history to reach the 500-goal milestone, behind their rivals Real Madrid.
The Blaugrana do have a way to go if they want to catch Los Blancos, who have scored 551 times in the Champions League.
Madrid have won more Champions League titles than any other team with seven, including the last three competitions.
Barca, on the other hand, have won the Champions League four times, but will have the opportunity to move closer to Madrid this season after the latter were knocked out of this year's competition by Ajax at the last-16 stage.
For Suarez, it was surprisingly his first Champions League goal of the season. The Uruguayan took nine games and 36 shots to finally get on the board in Europe in 2018-19.
The Uruguayan's last goal in the Champions League, ironically, came against the same goalkeeper against whom he scored on Wednesday night.
He found the back of the net against Roma in last season's quarter-final first leg, with Alisson, now Liverpool's shotstopper, conceding the goal on that occasion.