The hosts dominated the first half, with Andy Morrell testing Shrews goalkeeper David Button, while Ben Futcher headed against the crossbar from Mike Jones' left-wing cross.
Graham Coughlan then blocked Lowe's low cross before Terry Dunfield had to head behind after Futcher headed a Brian Barry-Murphy free-kick across goal.
Coughlan was alert again to clear off the line after Lowe's shot beat Button. But the Shrews responded after the break with Coughlan heading over,
while Dunfield tested keeper Wayne Brown with a long-range effort.
Shakers' skipper Stephen Dawson then went down under a challenge by Kevin McIntyre and Lowe stroked in the spot-kick. Button saved from Jones and sub Andy Bishop as Bury pushed for a clincher but Brown also had to deny Steve Leslie late on.