Twenty-one new 3,5-bipyridinyl-1H-pyrazole derivatives (pyrazolyl pyridines) have been synthesized and evaluated for their anticonvulsant activity in animal models of epilepsy. The pyrazolyl pyridines, 7–27, were obtained through a general one-pot synthesis, from ketones and acid chlorides via formation of 1,3-diketones in situ carried out in hydrocarbon solvent and LiHMDS base. The profile of anticonvulsant activity of final compounds was established in the maximal electroshock (MES) and subcutaneous pentylenetetrazole (sc PTZ) tests, after intraperitoneal injection in rats and mice, respectively, at doses of 30, 100, and 300 mg/kg. An observation was carried out at two different time intervals—0.5 and 4 h. Phenytoin was used as a standard antiepileptic against MES convulsions and valproic acid against sc PTZ convulsions. Furthermore, in addition to the primary anticonvulsant screening, the acute neurological toxicity was determined in mice by the rotarod test and in rats by positional sense test. The compounds showed anticonvulsant activity exclusively against MES convulsions. The compounds were found especially active in 100 mg/kg dose at both the time points, i.e., 0.5 and 4 h, depending upon the lipophilicity of molecules as indicated by statistically significant reduction in the time spent in tonic extension phase (p < 0.001). Further, the newly synthesized compounds were subjected to two-dimensional quantitative structure–activity relationship (2D QSAR) analysis through multiple linear regression, principal component regression, and partial least square regression analysis, and three-dimensional quantitative structure–activity relationship (3D QSAR) analysis by k-nearest neighbor molecular field analysis in conjunction with stepwise forward–backward, genetic algorithm, and simulated annealing variable selection methods using the software VLife MDS. The structure–activity relationship (SAR) as well as quantitative structure–activity relationship (QSAR) studies for anticonvulsant activity confirmed the crucial role of 3,5-bipyridinyl-1H-pyrazole core fragment for anticonvulsant activity.