A series of new molecules containing a thieno[2,3-d]pyrimidine scaffold was synthesized and characterized by adopting an efficient synthetic scheme. The effect of a free or substituted amino group at 2-position as well as an oxo-group, imidazole or 1,2,4-triazole ring at 4-position of the scaffold on the affinity and selectivity towards adenosine receptors (ARs) was evaluated. Compounds 17–19 with a free amino group at 2-position along with the presence of an imidazole/1,2,4-triazole ring at 4-position of the scaffold showed selective binding affinities for hA2A AR, whereas carbamoylation of the amino group at 2-position (in the presence of an oxo-group at 4-position of the scaffold) increased the affinity and selectivity of certain compounds (7–10) for hA3 AR. Molecular dynamic simulation study of one of the most active compound 8 (Ki hA1 > 30 μm, hA2A = 0.65 μm, and hA3 = 0.124 μm) revealed the role of important amino acid residues for imparting good affinity towards hA3 and hA2A ARs. Molecular docking studies were carried out for other compounds using the crystal structure of hA2A AR and a homology model of hA3 AR to rationalize their structure–activity relationships. The molecular docking results were in agreement with the experimental binding affinity data of ARs.