Can you buy tranquilizers for small house pets? I need to trim down the kitty.?

I am wondering if it is possible to buy a sedative or tranquilizer for a cat. I have this cat that is a total ***** when it comes to brushing. She has really long hair and it gets matted up with all kinds of things. Recently, with the rainy weather, she has been getting slugs in her fur. She's a loving cat and like to snuggle when she comes inside, but no one wants her on their lap with the whole outdoors in her fur. She can be brushed for about a minute before she starts going nuts. The matted up slugs and other bits in her fur cannot be brushed out. I had used scissors to cut a couple of the knots out, but there are many more left and she wont let all of them be cut out at once. She wiggles to try and get away, which is dangerous for her when there are scissors an inch from her belly. I really don't want to chance it any further so I would like to just buzz down all her belly fur. Is there any kind of sedative or remedy to knock out a cat so she can be groomed? Would a vet knock out the cat for me and let me take her home to be buzzed. How much should that cost? I don't want to take the cat to a groomer as their prices are ridiculous. I am not dropping $50 bucks to have my cat groomed, which is what the places are quoting around me here in California. For those of you whom will inevitably ***** about me not taking care of my cat or telling me to just pay up and have a groomer do it can bite me. Some people like to waste all kinds of money on their pets, but i already drop enough cash on my animals in food costs, toys, vet bills, etc.