Suarez joined Barcelona almost five weeks ago but fans have had to wait to welcome their new signing due to a four-month ban for biting Giorgio Chiellini at the World Cup.
While he will not be able to feature competitively until October 25, his suspension was last week relaxed to allow him to train and play in unofficial matches.
The Uruguayan was the star attraction at the Camp Nou on Monday night as Barca entertained Leon in the Joan Gamper Trophy, their traditional curtain-raiser to the new season, while there was further good news for the Catalan side as Brazilian forward Neymar started after recovering from the injury which ended his World Cup.
Suarez was paraded in front of the supporters with the rest of the team ahead of kick-off but started on the substitutes' bench and only came on in the 77th minute, earning a rapturous reception from the 72,475 in the crowd.
Barca had already carved out a commanding lead by the time Suarez entered the action, having opened the scoring after just three minutes when Lionel Messi finished off Neymar's cross at the end of a flowing move.
Neymar added a second in the 12th minute as he chipped a cool shot over the onrushing goalkeeper after latching on to a sublime threaded pass from Andres Iniesta which cut through the Leon defence.
The third goal arrived just before half-time and again it was Neymar, who rounded the keeper after being played in by Messi and then opted to back-heel the ball into the empty net.
Munir made it 4-0 ten minutes into the second half with a close-range finish at the back post after Dani Alves had raced on to a long Ivan Rakitic pass and squared the ball across goal.
Barca made six substitutions just after the hour mark but Suarez had to bide his time for another quarter of an hour before finally being introduced.
It was 5-0 moments later as Munir fired in his second of the night following good work from Spanish forward Sandro.
Suarez did not have much of a chance to make an impact in the closing stages as he was overshadowed somewhat by a tremendous team performance, and Sandro completed the rout with a powerful strike just before the final whistle.