Santa Cruz got on the end of Fredy Bareiro's flick-on to turn the ball into the net, as Nacional drew 1-1 with San Lorenzo in the first leg of the Copa Libertadores final in Paraguay.
San Lorenzo had led since the 65th minute thanks to a stunning volley from Mauro Matos but the Argentine visitors had to settle for a draw, after Santa Cruz's late heroics.
Bareiro flicked a long pass on with his head and Santa Cruz got to the ball ahead of his marker and San Lorenzo goalkeeper Sebastian Torrico, sliding in to score and spark pandemonium in the stands of the Estadio Defensores del Chaco in Asuncion.
San Lorenzo had the better of the first leg, with five of their 12 shots hitting the target, while the hosts shot six times but failed to test Torrico until Santa Cruz scored.
It was Nacional that created one of the best chances of the first half with a 27th-minute corner reaching Leonardo Caceres but the central defender could only stab his shot over the bar from six yards.
San Lorenzo's Emanuel Mas hit the post just after the half-hour mark but the visitors had to wait until 25 minutes remaining to claim the lead.
A neat move down the left eventually saw Julio Buffarini tee up Hector Villalba and Matos got to the winger's cross just ahead of his marker, hitting a volley around the corner that snuck inside the near post.
Having gone behind, Nacional began to look a bit more adventurous, although San Lorenzo appeared comfortable in defence until the third minute of second-half stoppage time.
Santa Cruz's strike ensures Nacional remain in the hunt for their maiden Copa Libertadores title, as both clubs look to lift South America's most prestigious continental club trophy for the first time.
San Lorenzo will host the second leg at the Estadio Pedro Bidegain on August 13.
