Round-up. It'll kill anything it gets on, so be careful (and you may have to re-seed the parts of the lawn that are being invaded) but you need to kill the plant right down to the roots. Grabbing handfuls as they appear won't do it, or at least, won't do it for a long, long time.

I hate to chance a herbicide because of the proximity of my collection of miniature conifers and a highly prized Japanese Maple, but its looking like I'll have to chance it to stop the spread of this stuff!

Apply the herbicide with a sponge.

Something else you can do is get a piece of cardboard to protect against overspray. Round-up won't hurt the other plants if it doesn't get on the leaves.

round up does not effect conifers and maples

Thanks for all the suggestions - it is supposed to clear up this weekend so I guess I'll try the RoundUp. Hopefully the wind will stay calm, as I have had some bad experiences in the past, which is why I am a little gun shy of using a herbicide. Even lost a prickly pear cactus one time due to spray drift. The sponge and cardboard ideas will probably come into play.

It has also been suggested by others to use a paint brush.

I think a sponge type paint brush might work. Do not know, but aren't there lawn products that only attack broadleaved plants and leave the grass alone? I thought that was how dandelions and plantain were controlled. Hope to use them in late winter, early spring,on a new lawn that is only recently sprouted, if they exist. Will read the labels.
While I was waiting for cooler weather, all sorts of broadleaf weeds grew, instead of grass.