Five goals from Messi, plus two from Tello, gave the Catalan club a 10-2 victory on aggregate after a 3-1 win in Leverkusen in the first leg of their last-16 tie.
The Argentina international had scored four goals against Arsenal in 2009-10, equalling the record of the likes of Marco van Basten and Simone Inzaghi, both of whom netted four times in a Champions League match.
Players with the highest number of goals in a single Champions League match:
Messi has now taken his tally to 12 goals in Europe this season, equalling Ruud van Nistelrooy's 2002-03 record for the most number of goals in a single edition of the Champions League.
The diminutive attacker, who is eight goals away from becoming Barcelona's all-time top scorer, is six goals ahead of Mario Gomez in the Champions League scoring charts.
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