Town battled to the end, but their one goal came too late to influence the outcome.
Notts, with two home debutants Lee Crooks in midfield and Eugene Dadi up front, played some of their most attractive football of the season in dominating the first 45 minutes during which they scored their goals.
The first, after 20 minutes, followed a splendid of piece of play by the highly promising Liam Needham whose left-wing cross found Dadi.
The effort from the new man came back off the post into the path of David Pipe who couldn't miss. It was Pipe's first goal of the season.
Notts constantly threatened to score a second which arrived after 37 minutes from Kelvin Wilson, who prodded home Chris Palmer's free-kick from close range.
Notts should have a third just before the break but Mike Edwards missed the target with a simple header.
Shrewsbury made two half-time substitutions. But Crooks and Julien Baudet missed simple chances for that elusive third goal.
The longer it went on the more the visitors threatened and two minutes from the end Colin McMenamin struck the base of a post with a overhead kick, leaving sub Kelvin Langmead with the simplest of scoring opportunities.
An afternoon punctuated by a series of extraordinary decisions by referee Ray Lee reached its climax with him disallowing a third Notts goal.
Jake Sheridan sent Pipe through the middle and he virtually walked the ball into the empty net with goalkeeper Joe Hart upfield. Mr Lee called play back for a foul on Sheridan, inexplicably ignoring the advantage rule.