The Argentine converted from the spot just 11 minutes into the quarter-final second-leg clash against AC Milan at Camp Nou on Tuesday, after he himself had been felled in the penalty area by Rossoneri defender Luca Antonini, and then struck again to take his tally for the current campaign to 14.
Messi had shared the previous record with former Manchester United striker Ruud van Nistelrooy, after netting 12 times in the tournament in 2010-11 when Barca won the trophy.
His current total is the most since the tournament evolved from the European Cup in the 1992-93 campaign.
The 24-year-old is now level, though, with Brazil-born Jose Altafini, who scored 14 times for Milan during the 1962-63 European Cup.
Messi's spot-kicks also took his overall Champions League tally to 51, making him the youngest player to rack up a half-century of goals in Europe's premier club cup competition.
The forward became the first player to score five goals in a single match in the 7-1 thrashing of Bayer Leverkusen last month and is also the all-time highest scorer in the competition's knockout stages.
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