Hartlepool started brightly and Steve Howard should have done better than head straight at goalkeeper Chris Weale from eight yards from a teasing cross from Jordan Richards.
Jonathan Franks then tried his luck from 25 yards with a well struck shot which Weale did well to help over the bar.
Shrewsbury gradually settled and, after Marvin Morgan twice forced saves from Scott Flinders, the breakthrough arrived in the 23rd minute.
Connor Goldson delivered a low cross from the right and Jon Taylor turned sharply to rifle home left footed from six yards to the bottom corner of the net, the winger's sixth goal of the season.
Hartlepool pulled level in the 55th minute with Wyke, on loan from Middlesbrough, delighted to see his low shot from 12 yards deflected past Weale. It was the first goal conceded by Shrewsbury for more than six hours.
Shrewsbury, now unbeaten in eight games, rallied in the closing stages and might have snatched victory had it not been for the brilliance of Flinders.
Having kept out a Dave McAllister drive, Flinders topped that with a stunning stoppage time save from Luke Summerfield's header with sub Tom Bradshaw smashing the rebound against the bar.