Suarez, named as a substitute at the Nou Camp, came on for the final 15 minutes in what was his first action since being banned for biting Giorgio Chiellini in Uruguay's World Cup game with Italy on June 24.
The striker was initially banned from all football activities for four months, but an appeal hearing last week allowed him to train with Barca and play friendlies.
Suarez, who cost Barcelona a reported 81 million euros ($108m) from Liverpool, will not be allowed to play a competitive game for his new club until after his ban ends at the end of October.
Attacking partner Neymar returned after fracturing a vertebra for Brazil in the World Cup quarter-finals against Colombia, and he coolly lifted the ball over keeper William Yarbrough for Barca's second after Lionel Messi had headed home the opener.
Neymar flicked in another before half time, and after the break substitute Munir El Haddadi netted twice and Sandro Ramirez, another youth product, completed the scoring a minute from time.
It was a new-look Barcelona that took to the field against Leon following an overhaul of the side for the La Liga season, which starts this weekend.
Barcelona's first season without silverware in six years has led to the arrival of Luis Enrique as coach. Suarez headed the list of reinforcements on the pitch.
Claudio Bravo started in goal following the departure of Victor Valdes, while another new signing, Jeremy Mathieu, partnered Javier Mascherano at the centre of defence.
Luis Enrique continued Barca's trademark 4-3-3 formation that also saw new faces Ivan Rakitic and Rafinha slot in comfortably.
There were plenty of changes in the second half, with Munir, in particular, excelling in front of goal, and he is another of Barcelona's youth products who will be pressing for a first-team place this season.