Gordon D'Arcy lifted the siege with a superb break, his kick ahead finding touch in the visitor's 22 and when the Pumas infringed Sexton landed the kick.
Tommy Bowe and Jamie Heaslip combined to send Stephen Ferris over for a clinically worked 19th minute try that Sexton converted and minutes later Contepomi missed the opportunity to get his side on the board when he was wide with a relatively easy kick.
Sexton extended the lead with a 28th minute penalty as the Pumas went offside and three minutes later Contepomi finally opened Argentina's account with a penalty from the 22.
Indiscipline had by now crept into the Argentine game and tug on Stringer's jersey by Rodrigo Roncero allowed Sexton another free shot at goal that he didn't waste.
Contepomi continued his abysmal kicking with a missed 37th minute penalty and in injury time another cheap penalty allowed Sexton put sixteen points between the sides at half time.
Ireland: 15 Geordan Murphy, 14 Tommy Bowe 13 Brian O'Driscoll (c) 12 Gordon D'Arcy, 11 Andrew Trimble, 10 Jonathan Sexton, 9 Peter Stringer; Cian Healy. Sean Cronin,Tony Buckley; Donncha O'Callaghan, Mick O'Driscoll; Stephen Ferris, David Wallace, Jamie Heaslip, Replacements: Damien Varley, Tom Court, Devin Toner, Denis Leamy, Eoin Reddan, Ronan O'Gara, Keith Earls.
Argentina: 15 Martin Rodriguez, 14 Horacio Agulla, 13 Gonzalo Tiesi, 12 Marcelo Bosch, 11 Lucas Gonzalez Amorosino, 10 Felipe Contepomi (c), 9 Nicolas Vergallo, 8 Juan Fernandez Lobbe, 7 Julio Farias Cabello, 6 Genaro Fessia, 5 Patricio Albacete, 4 Mariano Galarza, 3 Martin Scelzo, 2 Mario Ledesma, 1 Rodrigo Roncero.Replacements: 16 Agustin Creevy, 17 Marcos Ayerza, 18 Juan Figallo, 19 Santiago Guzman, 20 Alvaro Galindo, 21 Alfredo Lalanne, 22 Lucas Borges.