Employing single molecules as electronic circuit building blocks is one promising approach to electronic device miniaturization. We report single-molecule junction formation where the orientation of molecules can be controlled externally by the working electrode potential. The scanning tunneling microscopy break junction (STM-BJ) method is used to bridge tetrafluoroterephthalic acid (TFTPA) and terephthalic acid (TPA) molecules between the Au(111) electrode and the STM tip to measure the single-molecule conductance through the junction. When the Au(111) electrode is at negative potentials (with respect to the zero-charge potential), a highly ordered and flat-oriented superstructure forms, allowing for direct contact between the pi system of the benzene ring of the molecules and the Au(111) electrode, leading to junction formation with no anchoring group involvement. Our first-principles nonequilibrium Green's function (NEGF) computation shows a flat configuration yields a conductance that is 3 orders of magnitude larger than for a molecule vertically connected to the electrodes via anchoring groups. Conductances of 0.24 +/- 0.04 and 0.22 +/- 0.02 G(0) are experimentally measured with the flat configurations of TFTPA and TPA, respectively. These values are at least 2 orders of magnitude higher than the experimental values previously reported for the conductance of TPA bridged through carboxylic acid anchoring groups (3.8 x 10(-4)-3.2 x 10(-3) G(0)). In contrast, a positively charged surface triggers an order-disorder transition eliminating the high-conductance states, most likely because the formation of the flat-oriented junction is prevented. The dependence of TFTPA conductance on the electrode potential (electrode Fermi level) suggests a LUMO mediated transport mechanism. Calculation confirms the lack of an effect of the addition of an electron-withdrawing group are investigated.