Fill a teapot with water and put it over high heat until it comes to a full boil. While the water is heating up, make sure you have a clear path from the kitchen to the patches of weeds you need to kill. If children and pets are in the area, corral them somewhere else for the next few minutes.
Put on an oven mitt, just in case, and pick up the boiling teapot. Immediately take it outside and pour the entire pot of boiling water evenly over the troublesome weeds. If you didn't have enough water to fry them all, refill the pot and repeat the process.
Monitor the weeds closely over the next few days. The boiling water treatment will almost always completely kill growing weeds; after a few days, they will begin to rot all the way down to the root system. When the weeds look completely brown and dead, pull them out by hand. Pull them slowly and carefully, to give yourself the best shot at taking whole root systems with them.
Immediately spray the just-weeded cracks with a powerful commercial weed killer. The gaps you just created by pulling out the weeds and rotting out their root systems will provide the pores that are needed for the weed killer to penetrate.
Spray the problem areas about once a month during the late spring, summer and early fall to keep the problem from recurring.