The pace of Tom Bradshaw, one of three changes made by Town after their 3-0 defeat at Aldershot, troubled the County defence.
He beat the offside trap and rounded keeper Matt Glennon to score after 17 minutes.
Three minutes later he was through again but this time was brought down by Glennon. Nicky Wroe scored from the penalty to make Stockport's goal-against tally 90 for the season.
With County's 111-year stay in the football league at peril, they staged a second-half fightback but lacked a clinical finish.
James Vincent was inches wide and home keeper Ben Smith twice saved well from Anthony Elding. Bradshaw had a chance to improve Shrewsbury's goal difference near the end but lobbed over when clean through.
Source: PA
Source: PA