DNA G-quadruplexes (G4s) are now widely accepted as viable targets in the pursuit of anticancer therapeutics. To date, few small molecules have been identified that exhibit selectivity for G4s over alternative forms of DNA, such as the ubiquitous duplex. We posit that the lack of current ligand specificity arises for multiple reasons: G4 atomic models are often small, monomeric, single quadruplex structures with few or no druggable pockets; targeting G-tetrad faces frequently results in the enrichment of extended electron-deficient polyaromatic end-pasting scaffolds; and virtual drug discovery efforts often under-sample chemical search space. We show that by addressing these issues we can enrich for non-standard molecular templates that exhibit high selectivity towards G4s over other forms of DNA. We performed an extensive virtual screen against the higher-order hTERT core promoter G4 that we have previously characterized, targeting 12 of its unique loop and groove pockets using libraries containing 40 million drug-like compounds for each screen. Using our drug discovery funnel approach, which utilizes high-throughput fluorescence thermal shift assay (FTSA) screens, microscale thermophoresis (MST), and orthogonal biophysical methods, we have identified multiple unique G4 binding scaffolds. We subsequently used two rounds of catalogue-based SAR to increase the affinity of a disubstituted 2-aminoethyl-quinazoline that stabilizes the higher-order hTERT G-quadruplex by binding across its G4 junctional sites. We show selectivity of its binding affinity towards hTERT is virtually unaffected in the presence of near-physiological levels of duplex DNA, and that this molecule downregulates hTERT transcription in breast cancer cells.