In a match which featured two red cards, Callum Hoy went over in the closing stages to secure a 24-20 victory in Counties One Midlands West (North).
The two sides shared a penalty apiece in the first half, but it was Shrewsbury who got the only try to lead 10-3 at the interval.
Shrews added to their tally with a try early in the second half, but Stafford got themselves back into the game when Hoy muscled his way over for a try converted by Kevin van der Leest.
The visitors knocked over a penalty to push the score to 20-10 and, with Stafford only having 13 men on the pitch due to a red card and a sinbin the match looked to be all over.
But the hosts were roared on to one final effort as Stu Lewis touched down and Van der Leest converted, and then Nathan Caucau eventually shouldered his way through to release Hoy for a dramatic match-winning try, converted by Van der Leest.
Elsewhere in the division, Stourbridge Lions were beaten 43-7 on their own patch by Old Saltleians.
Meanwhile, Stourbridge’s disastrous start to the season continued as they suffered their third straight defeat to remain bottom of National Two West without a point to their name.
They did manage 19 points at Clifton – thanks to two tries from Jack Lea and one from Dallas Ororo – but the hosts also bagged 59 of their own.
Dudley Kingswinford picked up their second victory of the season in Regional One Midlands to sit fourth in the fledgling standings.
They were 36-17 winners at Nuneaton, running in five tries against the division’s bottom-placed side. Samuel Vaughan got the ball rolling with a penalty, and he went on to score a total of 11 points with his boot. But it was a flurry of tries in a 10-minute spell in the first half that really set up DK for the win as James Fildes, Jess Smith and James Ryan all crossed.
Mark Harrison went over five minutes after the interval, with Joseph Dunn getting their fifth and final try of the afternoon.
Newly-promoted Lichfield got their first victory of the season with a 39-22 triumph over Kenilworth.
The home side won the tries battle five to four, while Dave Lote contributed 14 points with the boot from four conversions and two penalties. Matt Cowley (two),Cal Turner, Fraser Goatcher and Sam Benson touched down.
Wolverhampton suffered their first defeat of the season to lose top spot in Regional Two West Midlands.
They were edged out 31-25 at Castlecroft, but still managed to pick up two bonus points – one for losing by less than seven points and another for bagging four tries.
Walsall kept a clean sheet as they saw off Malvern 42-0 thanks to tries from Will Hennessey, Michael Whitehouse, Liam Taylor, Corey Blackwood, Dean Ainger and Max Brown – as well as 12 points from the boot of Hennessey. But Old Halesonians were handily beaten 53-10 by Stratford Upon Avon.
Kidderminster are still searching for their first away win of the season in Counties One Midlands West (South) after going down 47-24 at Old Leamingtonians, who picked up their first positive result of the campaign.
Burntwood now have a record of one win, one draw and one defeat in Counties Two Midlands West (North) after a 19-19 result at Veseyans.
Aldridge went down 17-3 at home to Clee Hill and Handsworth defeated Luctonians Thirds 39-10.
In Counties Three Midlands West (North), third-placed Rugeley overcame Wednesbury 31-13 and second-placed Eccleshall edged out hosts Willenhall 12-5. Elsewhere, Cannock lost 33-19 at Aston Old Edwardians and Warley went down 62-11 at home to early leaders Trentham.
Counties Four Midlands West (North) leaders Stone were among the biggest winners of the day as they thumped Bloxwich 71-15 for their third straight bonus-point victory to start the campaign.
Second-placed St Leonards have a maximum score from two matches after downing Stoke-on-Trent Seconds 29-12.
Essington complete the top three after winning 26-14 at Linley.
Stourport were 44-8 winners to move up to third in Counties Four Midlands West (South).