Ian Rowe's Khalsa saw goalkeeper Sam Arnold given his marching orders after six minutes for taking out lively Pics striker Rackeem Reid.
And with no other shot-stopper in the squad, striker Josh McKenzie was forced to play the rest of the final between the sticks.
Liam McDonald's Rushall were not at their best but got the goals required as Tom Thorley headed home before half-time.
Kristian Green grabbed a second from close range on the hour mark to make sure they got their hands on the trophy.
Khalsa can be proud of their display in the circumstances. The Pics have won two of the last three Walsall Senior Cups.
Rushall – who were also champions in 2018 – went into the clash as favourites having finished fourth in the Southern Central Premier before falling short in the play-offs.
Khalsa, meanwhile, had an impressive first season a step below in the Northern One Midlands, finishing eighth, and possessed the quality to potentially cause an upset.
The chances of a surprise, however, were drastically reduced almost straight away.
Arnold came charging off his line, and in trying to stop Reid from latching onto a through-ball, he wiped out the striker for a straight red.
Khalsa – without a back-up keeper on the bench – had a mountain to climb.
Rowe's men, to their credit, kept their heads up and made themselves difficult to break down. Centre-forward McKenzie donned the gloves and made a few decent claims and clearances to help settle the nerves.
With half an hour on the clock, Rushall were still being given a good game.
The Pics had struggled to create anything clear-cut while Khalsa were working hard out of possession and assured when on the ball. Against the odds, they looked the better side.
McDonald would have been pretty disappointed with what he saw against the 10 men, but they did break the deadlock before half-time.
An impressive solo run from Tyler Lyttle saw him advance to the byline before cutting it back to Thorley, whose well-placed header sailed past the helpless McKenzie.
Still, Rushall were not entirely convincing. They were fortunate not to be pegged back prior to the interval, too, as Khalsa skipper Tes Robinson headed wide from Liam Armstrong's drilled free-kick.
Khalsa came flying out of the traps at the beginning of the second period as well.
Armstrong was put clean through, but having hesitated a touch, his one-on-one effort was diverted over by Jon Flatt.
The Pics then found a second to give themselves breathing room and, ultimately, put the result beyond doubt.
Lyttle was involved again as his free-kick to the far post found Sam Whittall, who headed the ball back across goal for Green to finish from point-blank range.
The final half an hour proved relatively fuss-free as Rushall were able to celebrate another Senior Cup success.