A cracking pace was set from the third minute when Matt Hamshaw, looking for his first Notts goal, delivered a swerving shot right on target which goalkeeper Luke Daniels palmed round his right-hand post.
Hamshaw had a part in County's opening goal six minutes before the break.
It was the first Shrewsbury had conceded this season and was achieved when Mike Edwards made Hamshaw's cross with a lovely glancing header.
It was no more than Notts deserved after they had dominated the opening 45 minutes in which they had six efforts on target to none by the visitors.
But Shrewsbury came out full of new determination at the start of the second half and within two minutes had levelled.
A free-kick against Michael Johnson was touched on by Grant Holt for Dave Hibbert to score from close range.
Both teams subsequently had chances, Darren Moss contributing one drive from 20 yards which Kevin Pilkington punched away.
Notts moved up a gear to apply stronger pressure on the visitors' rearguard and edged in front again on 75 minutes.
Delroy Facey fed the ball in and Richard Butcher did the rest from ten yards for his second of the campaign.
Shrewsbury nearly snatched an equaliser three minutes later when Holt's header was cleared off the line by Butcher, but then, two minutes from the end, they achieved another vital breakthrough.
Shrewsbury's two substitutes were responsible for salvaging a point. Chris Humphrey crossed from the right and Michael Symes at the back post bustled the ball into the far corner.
Even after that, in a pulsating climax, either Butcher or Facey could have won it for Notts who were left looking for their first league win.
Manager Ian McParland, sent to the stands in the second half for an alleged remark, declined afterwards to comment on the incident.