Argentina would have missed its first World Cup since 1970 if it had lost at packed Centenario Stadium.
But moments after Uruguay defender Martin Caceres was ejected for his second yellow card, Mario Bolatti scored amid a goalmouth scramble in the 84th minute to send a relieved Argentina to the finals in South Africa next year.
Argentina claimed the fourth and final automatic berth in South America, while Uruguay finished fifth and earned another chance to qualify through the playoffs next month.
Uruguay will meet the No. 4 team from CONCACAF, either Costa Rica or Honduras.
Brazil, Chile and Paraguay had earlier clinched the first three automatic berths, leaving Diego Maradona's much criticized team to venture to Montevideo, where Argentina had never won a qualifier in three previous attempts.
Argentina wound up fourth with 28 points, and Uruguay finished with 24, and Ecuador 23 after losing to Chile 1-0.
