Dampening timpani is not a complete art in itself, but it does take some practice to do well. The easiest technique is to use the pads of your fingers and palm to stop the vibration as you said, but things get slightly more complex than that. I find small quick circles with the hand on the drum head can make for a faster dampening and usually doesn't make too much extra noise. If you really need the sound stop stop quickly, you can use your entire forearm in addition to your palm.Also take note where you are placing your hand on the timpani (edge, center, middle, etc.) as each will give you a slightly different effect. I'd probably go for the area between the edge and the center for quickest stop of sound and least buzz, but you should still experiment on your own to see what works best.
Things get slightly more interesting when you have to continue playing while dampening or have to dampen multiple drums at once. You can usually use fingers 2, 3, and 4 for the dampen and regrasp the stick for another note very quickly. If you have to dampen three or more drums, try using both hands and your elbow for the last drum. I've even heard tell of some professionals using their legs and knees when 5 drums had to be dampened at once.
If you want to get really good results, you can buy woolen gloves, cut out the thumb and first, and wear them the entire time when you play. I've occasionally seen players have a good-sized piece of felt nearby to throw over the drum to mute it, but this usually isn't necessary. :D
Disclaimer: self answer!