The away victory moved them up to 10th place on 19 points from 16 games and confirmed they are slowly hitting top form a week after beating Bayern Munich.
Felix Magath's team, scoring only their second away win this season, have now won three of their last four league games.
Man-of-the-match Farfan struck on 30 minutes with a left-footed shot after Schalke saw Klaas-Jan Huntelaar's eighth minute penalty, awarded for a foul on Farfan, hit the post.
Mainz, more aggressive in the second half, wasted a huge opportunity to level in the 73rd minute when Andre Schuerrle's penalty, awarded when Adam Szalai was brought down, was palmed away by keeper Manuel Neuer.
Hungarian Szalai's deflected shot on the rebound sailed onto the crossbar with all the Schalke defenders helpless in the box.
Mainz are in fourth place on 30 points with Borussia Dortmund leading the standings on 43 following their 2-0 win over Werder Bremen on Saturday in their 14th victory in 16 games.
Earlier on Sunday, Freiburg striker Papiss Demba Cisse struck twice to lead his team to a 3-0 win over bottom-placed Borussia Moenchengladbach.
The 25-year-old Senegalese, who is now joint top scorer alongside Eintracht Frankfurt's Fanis Gekas with 13 goals from 16 games, headed them into the lead early in the first half.
He added another on the hour after Oliver Barth had given them a 2-0 lead four minutes before the break. Gladbach's fragile defence have now conceded 45 goals in 16 games.
The win lifted fifth-placed Freiburg to 27 points with one match left until the winter break. Gladbach are bottom on 10 with coach Michael Frontzeck's future at the team he also played for looking more and more uncertain.
