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Nanoarchitectural control of matter is crucial for next-generation technologies. DNA origami templates are harnessed to accurately position single molecules; however, direct single molecule evidence is lacking regarding how well DNA origami can control the orientation of such molecules in three-dimensional space, as well as the factors affecting control. Here, we present two strategies for controlling the polar (θ) and in-plane azimuthal (ϕ) angular orientations of cyanine Cy5 single molecules tethered on rationally-designed DNA origami templates that are physically adsorbed (physisorbed) on glass substrates. By using dipolar imaging to evaluate Cy5′s orientation and super-resolution microscopy, the absolute spatial orientation of Cy5 is calculated relative to the DNA template. The sequence-dependent partial intercalation of Cy5 is discovered and supported theoretically using density functional theory and molecular dynamics simulations, and it is harnessed as our first strategy to achieve θ control for a full revolution with dispersion as small as ±4.5°. In our second strategy, ϕ control is achieved by mechanically stretching the Cy5 from its two tethers, being the dispersion ±10.3° for full stretching. These results can in principle be applied to any single molecule, expanding in this way the capabilities of DNA as a functional templating material for single-molecule orientation control. The experimental and modeling insights provided herein will help engineer similar self-assembling molecular systems based on polymers, such as RNA and proteins.