Vince tucked home his penalty with just four minutes of the BetVictor Northern Premier League South East Division clash remaining.
It was his sixth successful spot kick conversion of the season as the midfielder kept his cool to send Worksop goalkeeper David Reay - who had defied the Daniels for large parts of the contest with a string of super saves - the wrong way.
The victory helped move Stamford within five points of league leaders Leek Town and eight clear of third-placed Cleethorpes whose games fell victim to the wet weather.
Stamford's match was one of just three in the South East Division to beat the elements with the strong gale-force wind again having a major say on proceedings at the Zeeco Stadium.
The Daniels made just one change to the opening line-up from their victory over Stocksbridge Park Steels in their last outing a fortnight ago with Jon Challinor being handed a start.
Stamford had the strong wind at their backs in the opening period and it was Challinor who created an excellent early opening.
He played in Cosmos Matwasa after the Worksop defence had misjudged Chitiza's initial pass, but the Stamford winger's shot was superbly saved by Reay at point blank range.
Worksop responded and Jordon Cooke had to be on hand to make a crucial clearance to turn away Steven McDonnell's low cross with Lynton Karkach waiting to pounce.
Reay was called into action again at the other end with another top-drawer stop as he dived full length low to his left to tip away Vince's curling shot that was destined for the bottom corner.
The Tigers felt they should have had a penalty midway through the half when McDonnell went down under Dan Haystead's challenge but referee Stuart Richardson waved away their appeals.
And just a couple of minutes later Stamford broke the deadlock through Tendai Chitiza.
Challinor got a vital touch, despite being caught by a follow through tackle, which allowed Chitiza to race clear and slot home past the advancing Reay.
Stamford were now looking to add to their tally by making the most of having the elements in their favour.
Reay had to punch clear at full stretch from two dangerous crosses while Tom Siddons struck the crossbar after an impressive turn and shot on the edge of the area.
Siddons went close again when he headed over from a Vince corner before Stamford's top scorer just failed to get on the end of Mike Armstrong's tempting cross to the back post.
The visitors then had a second penalty shout turned down when their appeals for a hand-ball by Sean Wright were spurned.
Tigers boss Kyle Jordan was booked for his protests as his side came out for the second half looking to make the most of having the strong wind at their backs.
McDonnell elected to shoot straight from kick-off which handed Dan Haystead a comfortable save as Stamford went on to create the better openings in the second period.
Chitiza flashed a shot wide of the far post after a strong run from Matwasa before Reay again denied the Daniels as his outstretched foot blocked another Chitiza shot after an astute through ball from Siddons.
Substitute Dec O'Hare then burst clear only for Reay to react well again with another fine save which looked to be even more crucial when the visitors levelled after 71 minutes.
Deegan Atherton's cross into the home box was headed home by McDonnell and, despite strong home protests for offside, the goal was allowed the stand.
This sparked the now customary strong response from Stamford with Reay again proving their nemesis with an acrobatic stop to keep out Matwasa's thumping strike.
James Blunden then sent a header from the resultant flag kick towards the bottom corner of the Worksop net, but Reay was again equal to the task to tip away the effort with arguably his best save of the game.
Stamford then lost O'Hare to a hamstring injury and it was his replacement Ollie Brown-Hill who won the penalty with just four minutes remaining.
Brown-Hill's surge into the box saw him upended by a clumsy challenge from Tigers captain Steve Wankiewicz and Vince did the rest by finally beating Reay for the second time to secure Stamford's 19th win from their 26th league game of the season.