and the green grass grows all around, all around

and the green grass grows all around, all around

Last summer, I Roto-Tilled a patch of grass—maybe 5' long by 3' wide—to make into a garden. Though small spurts of grass ended up coming back, for the most part the patch seemed content. I filled it with flowers and all was well in the world.
Fast-forward to now, when it appears the grass has returned with a vengeance. I'm going to Roto-Till the patch again once it's closer to flower-planting time, but here's my question for the garden-inclined; what can I do to keep the grass from growing back again next year? I know there's some black fabric-like stuff you can put in to keep weeds and things out, but I have zero experience with it & am not sure what all that would entail.
My budding green thumb thanks you for any help you can provide!
Pretty daisies.

Pretty daisies.

shasta daisy

shasta daisy

My room!

My room!

hi!

hi!

two-parter

two-parter

Question about my sedum!

Question about my sedum!