Regular Royals custodian Nick Draper was dismissed just before the hour mark after poleaxing Bradley Fortnum-Tomlinson in an incident that led to Stamford's second goal from the penalty spot.
His replacement Kris Taylor then saw red for felling Fortnum-Tomlinson when he was clean through with 16 minutes of the first qualifying round clash remaining.
Despite the double dismissal, Stamford were good value for their victory and boss Graham Drury felt they always looked in control against their Evo-Stik Premier Division visitors.
Drury said: "It was a good day at the office. We've scored three goals, kept a clean sheet and produced a professional performance which are good habits to have.
"The windy conditions spoilt the game, but it's a scalp for us against a higher level side. "We defended really well in the first half against the strong wind and, although scoring the second goal from the penalty spot has lifted us, I didn't think the sending offs effected the game.
"They started with one up top which showed they gave us a lot of credit. Even though we're a level below them, they saw us as a threat."
Drury was also full of praise for the performance of midfielder Mike Armstrong after his industrious display in the centre of the park.
He enthused: "I thought Mike was fantastic. His reading of the game and reacting to situations was superb.
"He was always first to the second ball and he's one of our unsung heroes. He does a lot of things that people don't always see, just by picking up the pieces. He made a big difference to us."
Stamford got off to a flying start as they went ahead after just two minutes when an astute pass from Pearson Mwanyongo released Fortnum-Tomlinson who raced clear before clipping his shot over the advancing Draper.
The visitors, despite having the elements in their favour in the first half, rarely made an impression with Kris Taylor flashing a free-kick wide being their only notable effort.
Jordan Smith headed wide following good work from Fortnum-Tomlinson who then fired over himself after a good move involving Rob Morgan and Eliot Putman. Stamford took the game to their visitors after the break as Henry Eze came close to doubling their lead with an audacious long distance thunderbolt that rattled the crossbar with Draper well beaten.
The Daniels second goal came shortly after as Fortnum-Tomlinson raced away but, after knocking the ball past Draper, he was flattened by the Royals goalkeeper. Draper was dismissed and Mwanyongo stepped up to confidently stroke home the resultant penalty past stand-in Taylor.
Taylor's stint in between the sticks though lasted just 15 minutes when he came racing off his line and took out Fortnum-Tomlinson who had broken clear.
He was red carded and skipper Danny O'Callaghan took over as Stamford piled on the pressure with Eze heading just wide while Putman's excellent run saw James Beresford make an excellent block to deny the Daniels.
Substitute Joe Burgess also saw an effort superb kept out by Nathaniel Kelly's challenge before fellow replacement Sam Hollis put a gilt-edged chance over the bar after a good move involving Lee Clarke and Armstrong.
Stamford wrapped up the victory in the 90th minute when Ben George started and finished a good move down the right with a low shot that beat O'Callaghan at his near post and rubber-stamp the Daniels' place in the second qualifying round on November 11.