The Bards struck twice in the final 14 minutes to secure their first away win of the season after Stamford had twice recovered with goals from Jack Duffy and Ashton Offler after falling behind.
Stamford made four changes to their starting line-up following Saturday's defeat at Halesowen with Billy Bennett, Harry Wood, Rob Morgan and Ollie Brown-Hill coming in for Connor Bartle, Mikey Armstrong, Trey Charles and Ricky Miller who faces more than a month on the sidelines due to an ankle injury.
The Daniels went into the game on the back of Saturday’s league loss and the FA Cup reversal at Harborough and it was the visitors who started the brighter of the two teams.
They took just eight minutes to break the deadlock as home goalkeeper Dan Haystead could only palm an inswinging corner out as far as Callum Ebanks who drove home the rebound.
Tom Solanke smashed a shot just over moments later before Stamford started to grow into the contest.
They levelled after 15 minutes when their setpiece caused problems for the visitors and Bennett's corner sparked a scramble with Duffy prodding home the rebound from close range.
Stratford came closest to regaining the lead as the half progressed with Riley O'Sullivan being thwarted by a fine stop from Haystead after Ashton Offler had misjudged a long clearance.
Haystead turned away a low shot from Ebanks before the Bards regained the lead two minutes before the interval.
The visitors were awarded a hotly-contested free-kick with Stamford's appeals for hand-ball falling on deaf ears.
The quickly-taken setpiece found Alex Worley who raced forward before curling home a sublime finish into the far corner from outside the area.
Stamford could have restored parity in first half injury time as Lee Shaw burst into the area but his low shot was touched past the post by Bards goalkeeper Liam O'Brien.
Ebanks stung the palms of Haystead early in the second half while Dan Lafferty headed a cross straight at the Daniels goalkeeper with Joe Burgess steering a shot wide following a corner at the other end.
Stamford continued to push for an equaliser as the half wore on and it arrived after 69 minutes as Harry Vince linked well with Shaw before drilling in a low cross which was turned home by Offler.
Stratford looked for an immediate response and substitute Jack Storer dragged a shot wide before they hit the front for the third time as the game approached the final 15 minutes.
O’Sullivan was the provider with a teasing run before setting up Jonny Ngandu who clipped his finish into the far corner of the home net.
A fourth goal followed six minutes later as the powerful Ebanks burst into the box before teeing up Lafferty for a simple finish.
There was no way back for the Daniels who suffered a further setback after the final whistle when Bennett was dismissed as his frustrations at the performance of referee Alistair Wilson finally spilled over.