The Argentine World Player of the Year became the first player to score five in a Champions League match. Substitute Cristian Tello scored twice as the holders equalled the biggest victory margin in the knockout stages of the competition.
Messi, who did not appear to have a bead of sweat on him after the match at the Nou Camp, took his tally to 12 goals in seven Champions League appearances this term, equalling the record for a single season he shares with former Manchester United striker Ruud van Nistelrooy.
All five strikes against a hapless Leverkusen, including brilliant dinked efforts with either foot, showcased the stunning skills honed in Barca's youth academy that have won him the World Player award for the past three years.
"The important thing is what the team did and that we qualified for the next round," a typically modest Messi said in a television interview.
"It's nice to score five but winning was the priority," added the 24-year-old, clutching the match ball and smiling shyly.
After they lost last month's round of 16 first leg in Leverkusen 3-1, the Bundesliga side's mission impossible was effectively ended when Messi sped on to Xavi's lofted pass and brilliantly scooped the ball over Bernd Leno in the 25th minute.
Tello netted twice either side of Messi's fourth, which came after Leno spilled the ball at his feet, and the Argentine wizard bagged his fifth with a powerful strike six minutes from time before Leverkusen substitute Karim Bellarabi scored in added-time.
Messi has been enjoying a purple patch in recent weeks, even by his lofty standards, and Wednesday's goals mean he has scored 14 in his last five matches for club and country.
"He is a unique player," Barca coach Pep Guardiola told a news conference.
"Scoring five goals is not easy but if Leo sets himself the task of scoring six one day he will certainly do it."
Guardiola's Leverkusen counterpart Robin Dutt cut a lonely figure on the touch-line in the second half as he watched his side struggling to compete with the Spanish, European and world champions.
"There is no question that a reverse of that magnitude really hurts," Dutt said. "There are scarcely words to describe the way Messi plays.
"Barcelona are the best team in the world even without Messi but with him they are almost in another galaxy.
