I have done this successfully over and over, so it's worth sharing.
On a bright, sunny day put plain, cheap-o white vinegar into a spray bottle.
In the early morning, heavily spray the weeds paying close attention to saturating the base of the stem at ground level.
The weeds will wither and die with no chemicals needed! Results will begin right away but the weeds will die over a few days' time as their roots are destroyed by the vinegar.