Argentina's Gabriel Batistuta and Ramon Bello put the home side in control with two first-half goals, but Roberto Palacios pulled one back in the 68th minute to inflict a tense finale on the home fans.
Argentina lead the group on goal difference from Colombia, who drew 1-1 in Paraguay. The winners of the group qualify automatically for the finals next year, while the runners-up play off against Australia for a place in the United States.
Batistuta turned his marker and ran on to place his shot calmly beyond Miguel Miranda, Peru's brave goalkeeper, for the opener in the 32nd minute. Six minutes later Bello converted Batistuta's cross with a slick back-heeled strike. However, Peru, who have lost all their games to date, launched a determined comeback that saw Argentina adopt time-wasting tactics in the closing stages.
In Asuncion, the experienced Fredy Rincon gave Colombia a first-half lead, but Catalina Rivarola levelled soon after the break.
In Group B, Bolivia maintained their 100 per cent record with a 7-0 demolition of Venezuela in La Paz. They have scored 20 goals in five games: on Sunday Milton Melgar and Marco Etcheverry each hit two with William Ramallo, Erwin Sanchez and Marco Sandy adding one apiece.
Brazil, happier now that they have completed their away programme, moved in to second place with a 2-0 win over Ecuador in Sao Paulo. They trail Bolivia by four points in the group, from which the top two qualify. Bebeto, from the Spanish club, La Coruna, scored the first goal in the 34th minute and set up the second for Dunga, after 56 minutes.
Bebeto apart, though, Brazil lacked creativity against a negative Ecuador side. The home fans showed their displeasure, and the newspaper Folha de Sao Paulo declared: 'Brazil is obtaining its qualification without brilliance, without emotion, as if it were carrying out a ritual.'Reuse content