Farfan scored the winner after 12 minutes, combining brilliantly with Lewis Holtby to chip in his sixth goal of the season and send his team to the head of the standings on 34 points from 17 matches.
"We made our own life difficult," Schalke coach Felix Magath, who took over after steering VfL Wolfsburg to last season's title, told reporters.
"We should have used our chances after taking the lead to be more comfortable. We did improve but lacked that killer instinct. I am glad though our lead was enough until the end."
Schalke wasted a clear chance to take the lead on 11 minutes when Ivan Rakitic was left unmarked in the box four metres out but failed to head a Farfan cross on target.
The Peruvian striker then took matters into his own hands a minute later, finding Holtby at the edge of the box, who sent a through ball for Farfan to chip over keeper Heinz Mueller.
Croatia international Rakitic was again unlucky minutes later when he curled a corner kick on to the bar.
Schalke, who have now won three matches in a row, gradually forced Mainz to come forward and lurked to hit on the break.
Kevin Kuranyi, fighting for a return to the Germany squad, missed two clear chances while captain Heiko Westermann should have made it 2-0 in the 65th minute when he headed wide another curled Rakitic corner.
