Winners of the Clausura title in the second half of the season with a record run of 14 wins and one draw, Penarol lifted the trophy 2-1 on aggregate. Nacional won the season opening Apertura championship in December.
Celebrations by fans of Penarol, one of the country's big two clubs, were marred by violence in central Montevideo.
Central defender Alejandro Lembo put Nacional ahead in the 35th minute when he headed in a corner before Aguirregaray equalised in the 68th minute.
Penarol had midfielder Gaston Ramirez sent off in the 79th minute and Nacional substitute forward Sergio Blanco was also shown the red card three minutes from full-time.
Coach Diego Aguirre was in charge when Penarol last won the title in 2003 and he was at the helm again this year, appointed after the team had a disappointing Apertura.
"There was a need to be champions, Penarol needed to win, the happiness is incomparable. This is a moment of glory," former Penarol player Aguirre told reporters.
"We had a great championship, we beat all the teams and that's exceptional."
