After many years of self-doctoring more cuts than I'd like to admit, what I've found is this. On any cut, especially a deep one, you need to clean it and get the edges back together as soon as possible. To hold them that way, the best way I know is tape. It's fast, easy to apply, easy to carry and it works. Done quickly and properly even deep wounds will reconnect amazingly fast. And once you get it together, leave it that way as long as you can! If you still feel the need to use gauze, put it over the top of the tape.
The old style white adhesive tape is a waste of time. Use a real surgical-type tape. I like the 3m "Transpore". My wife brought some home from the hospital after some recent surgery to hold dressings in place and I've used nothing else ever since, it's good stuff. Alternatively, you can use duct tape or believe it or not a good cellophane tape (which has the other advantage of being see-through).
Getting it off can sometimes be a problem. Pulling the tape can tend to pull the wound open too if you're not careful. If I have the time, I'll tear off a narrow piece of tape and put it glue-to-glue in the middle of the main piece, to create a kind of butterfly-type bandage. That way the adhesive is held away from the edge of the wound and gives you a place to cut through when it's time to remove or change it.