The defeat leaves the Daniels 10 points adrift of a coveted top five finish with just 10 matches of the Evo-Stik League Division One East season remaining.
Goals at either end of a disappointing contest gave the vistors the spoils as Stamford suffered their third home league loss of the season.
The reversal left manager Graham Drury lamenting the absence of suspended striker Gregg Smith while the Daniels boss was also 'adamant' his side should have been awarded a last-gasp penalty before Ossett's second goal when the ball appeared to strike Tyrone Gay's arm in the box.
Drury said: "It was really frustrating because Kern (Miller) has headed the ball against the back of their players head for the first goal. It's hit him and gone in.
"That bit of luck has gone against us for the first goal because I didn't think there was a lot in the game.
"The first goal was unfortunate and they've got a second late on when we've gambled.
"The two really key points were that we're unfortunate with the first goal and I am adamant that was a penalty at the end because his arm has moved towards the ball.
"The game has been a battle all over the middle of the park.
"I thought it was a poor game overall. It was very scrappy with two sides who both went hammer and tongue at it.
"Credit to Ossett because they have come here and done a good job. It's only the fourth league game we've lost at home in two seasons.
"I thought they were strong and they looked a physical side all over the pitch with good players who had good movement.
"When you've got that presence up top like they have, it shows how much we're missing Gregg Smith.
"It was a massive blow to lose the game and I can't emphasise how much losing Gregg was massive for the way this team play.
"It's killing us as a football side at the moment because I thought we had solved the problem.
"I don't believe we would have dropped points at Spalding if Gregg had played because I believe we would have defended the setplays better if he had been there.
"It sounds a lot, but I just don't think we've got a platform to build off in the final third.
"We're asking Joe Boachie and Ryan Seal to play with their back to goal when we know they are runners who go beyond.
"We're asking them to do something they're not used to. It's not their faults, but it means we have to find something different because we've lost that player.
"I've perhaps learned a massive lesson in that I need to bring in two of those type of players in case this happens again.
"We've got to dust ourselves down and now go into a real tough programme against second and third in the league.
"We haven't got that player we were hoping to have in the team and, if you haven't got it, you've got to a find a way of doing it.
"Training sessions next week are going to be on patterns of play of trying to get into the final third and get runners in beyond and try and join in with links.
"It's tough at the minute without that striker though, it really is."
Stamford handed a first start to Peterborough United loanee Jack Gurney in their only change to the starting line-up from last week's 2-2 draw at Spalding.
The visitors created the first openings with Tom Greaves crowded out when getting a sight of the home net while Dan Haystead was forced to
make a hurried clearance as Karl Jones converged on his goal.
But it was the Daniels who had the ball in the net first as Gurney's low cross into the box saw Ossett struggle to clear their lines with Ryan Seal smashing the loose ball home only for the assistant referee's flag to disallow the effort for offside.
And shortly afterwards Stamford found themselves trailing to Jones' ninth minute opener.
Jordon Cooke had produced a superb clearance to deny Jones an almost certain tap-in but, from the resultant corner, Miller headed the ball against the Ossett marksman whose effort looped into the home net off the underside of the crossbar.
Stamford responded with Seal seeing a shot deflected narrowly wide off James Knowles with Joe Burgess then going down under a clumsy challenge from Corey Gregory from the ensuing corner, but referee Jacob LeHane waved away the Daniels' appeals for a penalty leaving Ossett with the advantage at the break.
The visitors had a strengthening wind at their backs in the second period and started brightly with Greaves just failing to convert a dangerous cross from Aidan Chippendale while Gregory cracked an effort against the Stamford crossbar after the home side had struggled to clear their lines.
Chippendale also smashed another effort just over as Stamford began to push more men forward in search of an equaliser.
Miller was moved into the attack and he caused problems from a corner in the dying throes with the ball pinging around the Ossett box which sparked further strong Stamford penalty appeals for hand-ball after hitting Gay who cleared under pressure.
Referee LeHane was again unmoved though and Ossett made the most of it by breaking clear to tee up Greaves who rifled home a fine finish
into the bottom corner in the sixth minute of stoppage time.
The goal sparked a melee between both sets of players with the visitors seeing James Burke dismissed for his involvement.
But, despite finishing the match with 10 men, the sending off failed to take the shine off an excellent away success for the visitors which leaves Stamford with an uphill battle to now reach the play-offs.
# | Team | Pl | Pts |
9. | Belper Town | 38 | 59 |
10. | Marske United | 38 | 58 |
11. | Stamford | 38 | 50 |
12. | Frickley Athletic | 38 | 48 |
13. | Stocksbridge Park Steels | 38 | 43 |
14. | Lincoln United | 38 | 43 |
15. | AFC Mansfield | 38 | 42 |