Combining first principle density functional calculations and Moriya's self-consistent renormalization theory, we explain the recently reported counterintuitive appearance of an ordered magnetic state in uniaxially strained Sr$_2$RuO$_4$ beyond the Lifshits transition. We show that strain weakens the quantum spin fluctuations, which destroy the static order, more strongly than the tendency to magnetism. A different rate of decrease of the spin fluctuations vs. magnetic stabilization energy promotes the onset of a static magnetic order beyond a critical strain.
