Russia led the tie 22-21 after the first leg, and were ahead at half-time in Montevideo, but three tries in the second half saw Uruguay home.
Los Teros qualify for the World Cup, which will take place in England and Wales, for only the third time.
They will face England, Australia, Wales and Fiji in Pool A.
Fly-half Felipe Berchesi kicked 21 points for the hosts, with Joaquin Prada, Alejo Corral and Agustin Ormaechea crossing for tries.
Aleksandr Ianushkin's try just before the break had put Russia 17-12 ahead, but after a penalty increased their lead, Prada's try began the decisive phase of the match.
Yet despite Uruguay's three tries, when Yuri Kushnarev converted Vasily Artemyev's try with three minutes left, Russia were a converted try away from winning the tie.
But a penalty from Berchesi in injury time secured Uruguay their place at the World Cup, where they will face Wales in their opening match on 20 September in Cardiff.
Uruguay qualified for the 2015 Rugby World Cup by beating Russia 36-27 in the second leg of their play-off to claim a 57-49 aggregate victory.