The Pumas captain cancelled out an early penalty from Kristopher Burton, but the 21st-minute sin-binning of Julio Farias-Cabello paved the way for the Azzurri to go in 10-3 front with a converted penalty try.
However, Argentina responded with Tomas Leonardi dotting down while Contepomi continued to be accurate with his boot as the home side opened up a 15-10 lead at the interval.
Contepomi then added another penalty at the start of the second half, but Italy hit back with a try from Edoardo Gori after 53 minutes to close the deficit to three points.
The Pumas soon pulled away though, with Rodrigo Roncero, Leonardo Senatore and Contepomi all touching down before Mauro Bergamasco grabbed a late score for Italy, which Riccardo Bocchino converted, to give the result less of a one-sided look.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.