Farfan's first-half strike, in a match which pitted two Argentine coaches against each other, was also the first goal that Paraguay have conceded in the competition.
Peru desperately needed a win after losing their first two games and coach Ricardo Gareca fielded Farfan, Jordy Reyna, veteran Claudio Pizarro and Paolo Guerrero in an ambitious four-man attack.
Guerrero was close to giving Peru an early lead when he ran onto Renato Tapia's diagonal through ball but fired his effort just wide of the goal.
Peru, who have not qualified for a World Cup since 1982, survived a scare when goalkeeper Diego Penny was caught off his goalline at a corner and Yoshimar Yotun headed the ball off the line.
The hosts broke through in the 20th minute when Guerrero found Farfan completely free on the left and the former Schalke 04 forward controlled the ball and fired a low shot just inside the near post.
Guerrero and Pizarro were both agonisingly close for Peru with headers just before halftime.
Paraguay, who qualified for four World Cups in a row between 1998 and 2010 but missed out on Brazil last year, evened the match up in the second half but did not carry a threat.
"I liked the commitment of the players with the country and the national team because there was a lot at stake and we were facing very difficult opponents," Gareca told reporters.
Paraguay coach Ramon Diaz said: "I didn't like our performance and we have to improve, although I liked our attitude."
The 10-team group, where four teams qualify directly for Russia in 2018 and the fifth plays off against the winners of the Oceania group, is already developing into a highly unpredictable contest, with both Brazil and Argentina having made poor starts.
Ecuador, the only team to have won their opening three matches, lead with nine points, followed by Chile (7) and Uruguay (6). Brazil, Paraguay and Colombia have four each, Peru and Bolivia three, Argentina two and Venezuela are pointless.
(Writing by Brian Homewood in Berne. Editing by Patrick Johnston)
