We introduce a versatile method that allows local and repeatable delivery (or depletion) of any water-soluble reagent from a nanopipet in ionic solution to make localized controlled changes in reagent concentration at a surface. In this work, Na+ or OH- ions were dosed from the pipet using pulsed voltage-driven delivery. Total internal reflection fluorescence from CoroNa Green dye in the bath for Na+ ions or fluorescein in the bath for pH quantified the resulting changes in local surface concentration. These changes had a time response as short as 10 ms and a radius of 1-30 mu m and depended on the diameter of the pipet used, the applied voltage, and the pipet-surface separation. After the pipet dosing was characterized in detail, two proof-of-concept experiments on single cells and single molecules were then performed. We demonstrated local control of the sodium-sensitive flagellar motor in single Escherichia coli chimera on the time scale of 1 s by dosing sodium and monitoring the rotation of a 1 mu m diameter bead fixed to the flagellum. We also demonstrated triggered single-molecule unfolding by dosing acid from the pipet to locally melt individual molecules of duplex DNA, as observed using fluorescent resonance energy transfer.