For Leeds, who won the Championship last season, this was a step closer to securing their top-flight status for another campaign, although they will be hugely disappointed to have not held on for all three points.
They looked to be in trouble at the end of November but since December they have collected 20 points from 14 games, only losing twice in that period.
Before the 3-1 win over Nottingham Forest at the beginning of the month, Farke said they needed 12 points to ensure survival - and they now have five of those after a win and two draws.
Although the manner of Anton Stach's wonderful strike surprised most of those in a sold-out Villa Park, the visitors had been good value for their lead with 10-goal top scorer Dominic Calvert-Lewin a constant handful.
On the first of two good chances, a heavy touch enabled Ezri Konsa to recover and make a perfectly-timed sliding challenge. Calvert-Lewin's touch was much better on the second occasion as he raced on to Jayden Bogle's well-weighted ball over the top, only for Calvert-Lewin to be denied by Emi Martinez's excellent save.
In the second half, Leeds had to defend deeply but did create a couple of chances.
Calvert-Lewin had an effort saved by Martinez, who also saved a diving header from Lukas Nmecha, and the failure to score a second proved costly.