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Evans pulled off a trio of brilliant stops in open play, before saving an injury time penalty to prevent the Shrews earning a replay.
Shrewsbury player boss Jimmy Quinn was disappointed to end up on the losing side.
Scunthorpe dictated most of the first half but only had one goal to show for all their efforts and that came a early as the ninth minute when Steven MacLean's shot was pushed out by Scott Howie, but Paul Hayes followed up to score.
Quinn headed down for Luke Rodgers to fire straight at Evans and then Andy Butler blocked a shot from Kevin Street.
Midway through the second half Shrewsbury began to show as being the better side and Evans turned over a header from Quinn before pulling off two brilliant stops from Jamie Tolley.
Scunthorpe almost added to their tally on 80 minutes when Peter Beagrie fired in a shot which flicked off the bar and over.
But then came an exciting finale as Quinn grabbed an 86th minute equaliser.
A replay looked inevitable until Paul Hayes managed to drive in his second goal on 90 minutes.
Three minutes of injury time saw Shrewsbury hit back once again and when Terry Barwick was adjudged to have handled in the box, up stepped Colin Cramb, but Evans covered himself in glory by saving his spot-kick.