Nestor Ortigoza made no mistake from the spot nine minutes before half-time after Nacional's Ramon Coronel had blocked a shot in the penalty area with his hand, and San Lorenzo held on to their 1-0 lead throughout the second half as the visitors became more desperate.
The home win was enough for San Lorenzo to end their 54-year wait for Copa Libertadores success, after they had claimed a 1-1 draw in Paraguay last week.
San Lorenzo were the first Argentine club to qualify for the Copa Libertadores in 1960 - the competition's inaugural year.
But the Buenos Aires-based club had to wait until Wednesday to win South America's premier continental club competition, becoming the ninth team from Argentina to achieve that feat.
The two-legged final turned in the 34th minute when a corner for San Lorenzo reached the back post where Martin Cauteruccio attempted to centre the ball for the home side with an overhead kick, only for Coronel to block it with a hand raised above his head.
Despite a mass protest from Nacional, the referee had no choice but to award the penalty and Ortigoza continued his brilliant record from the spot, slotting his effort into the bottom right corner.
The Paraguayan midfielder has scored 21 of 22 penalties in his professional career.
Nacional missed two chances late in the first half and had a couple of shots blocked after half-time but were unable to properly test San Lorenzo goalkeeper Sebastian Torrico throughout the match as the hosts held on to lift the trophy.
The final whistle sparked massive celebrations at the Estadio Pedro Bidegain with fans jumping in unison throughout the Buenos Aires venue.
San Lorenzo's triumph made them the first club since Sao Paulo in 1993 to win the Copa Libertadores without claiming a single victory away from home.