Barcelona held a 3-1 lead from the first leg in Germany, and Messi put the Spanish champions in a commanding position with two strikes before half-time.
The Argentine striker completed his hat-trick in the 49th minute, before Barcelona debutant Cristian Tello scored a brace – but the night belonged to Messi, who scored his fourth and fifth goal to cap the rout.
“Tonight we witnessed one of Lionel Messi’s most special nights,” said Guardiola. “Watching it was like receiving a gift.
“He deserves to be honoured right now because it’s something really incredible that he is now just seven goals behind [Barcelona’s all-time top scorer] César Rodríguez – he’s only 24.
“It’s not easy to score five goals in a single game and that’s coming from someone who scored 11 in his entire career.
“If he wants to, he’ll score six one day. I have to also say that Andrés Iniesta played magnificently too.”
And Guardiola hailed his side’s performance against Leverkusen as Barça reached the quarter-finals of Europe’s premier competition for the fifth successive year.
“This really is the most beautiful competition,” added Guardiola. “The team we were facing tonight eliminated Valencia and only a few days ago beat Bayern München; that speaks volumes of our achievement.
“We have to thank all of the players and the staff at the club.”