Barcelona went into half-time 1-0 up against a PSG team that was unable to call on Zlatan Ibrahimovic, Marco Verratti and Serge Aurier thanks to Neymar's goal in the 18th minute.
Suarez took centre stage in the second half and scored in the 67th and 79th minutes to make it 3-0.
However, PSG grabbed a consolation goal in the 82nd minute when Barcelona defender Jeremy Mathieu scored an own-goal.
With his brace Suarez has now scored 11 goals in his last 11 matches.
What made these two goals more special, in the striker's opinion, is the fact that he nutmegged Luiz twice in the process.
"Forwards are always trying to look for goals, and two good moves came off for me," Suarez told Canal Plus. "I had to do the two nutmegs, because it was the only option I had. A nice move came off, and the ball went in.
"We three forwards can play in any of the three positions, so we can switch around. Leo also comes into the centre and space opens. That is why the goal came from the right wing."
But, Suarez made it clear that Barcelona cannot afford to take their foot off the pedal during the second leg, which will be played at the Nou Camp on April 21.
"In football you never know what can happen," he said. "They have a lot of quality and we must be aware that this is not over yet. It will be a nice game."