Brady was calm during his walkout while Edwards jogged briskly towards the octagon.
Edwards spent much of the fight on the backfoot against Muhammad in July and it was Brady who was the busier fighter in the early stages, landing a couple of one-two punch combinations.
Edwards found a home for two uppercuts to the body, but ended the round on the receiving end of the first takedown of the fight.
Brady’s dominance in the grappling department continued into the second and third round as he controlled the action on the ground, with frustration in the crowd starting to grow.
Before the fourth round Brady’s corner told him “Edwards is broken” and the American took advantage, taking the action to the ground once more and securing the fight-ending guillotine choke.
As Brady celebrated, Edwards lay crestfallen on his back on the canvas with his hands on his head.
“I heard all week people saying I’m too small. I’m not small for welterweight, I was 190lb when they weighed me at the back. I’m just short and that’s alright,” added Brady.
The win was Brady’s third in a row as he thrust himself into title contention, while Edwards slips further away from his dream of becoming Britain’s first two-time UFC champion.
Elsewhere there were was an impressive win for England’s Nathaniel Wood as he outpointed France’s Morgan Charriere, while Scotland’s Chris Duncan submitted England’s Jordan Vucenic in an all-British contest.
