Defender Ramiro Funes Mori put Argentina ahead after 15 minutes but was responsible for Peru's late penalty equaliser that was converted by Christian Cueva.
In between, Peru's veteran striker Paolo Guerrero equalised early in the second half and Gonzalo Higuain restored Argentina's lead in the 77th minute.
After nine matches, the halfway point in the South American qualifiers, Uruguay top the table with 19 points followed by Brazil on 18 and Ecuador, Colombia and Argentina all on 16. Peru climbed one place to eighth with eight points.
The top four go through to the 2018 finals in Russia while the team in fifth place, currently Argentina on goal difference, qualify for an intercontinental playoff against the Oceania winners for another berth.
Peru almost scored early in an entertaining, even match at the Estadio Nacional when defender Renato Tapia sent a glancing header from a corner just wide in the ninth minute.
At the other end, Pedro Gallese made a diving save from Sergio Aguero's 10th-minute free kick in front of the posts.
Five minutes later Argentina were ahead when Peru failed to clear a corner and Funes Mori steered a shot into the bottom corner.
Sergio Romero blocked a stinging shot from Guerrero as Peru built quick counter-attacks and Cueva was close with a free kick.
Peru carved out a chance for Edison Flores five minutes into the second half but the forward was slow to take a shot and was blocked.
Eight minutes later, though, the home side were on level terms when Guerrero reached a cross from the left, fended off Funes Mori and shot past Romero.
With 13 minutes to go, Higuian took a pass from Pablo Zabaleta on the right of the box and deftly chipped past Gallese for his 32nd Argentina goal.
Funes Mori turned villain when he tripped Guerrero in the box and Cueva scored a deserved equaliser with the 84th-minute penalty.
Bookings for Nicolas Otamendi, Zabaleta and Funes Mori mean they will be suspended when Argentina host Paraguay on Tuesday with coach Edgardo Bauza having to field an almost entirely different back four.
(Writing by Rex Gowar; Editing by Greg Stutchbury)
