New sets of ibuprofen and indomethacin conjugates comprising triazolyl heterocycle were synthesized via click chemistry, adopting an optimized protocol through the molecular hybridization approach affording the targeted agents in good yields. The new non-steroidal anti-inflammatory drug (NSAID) conjugates were designed and synthesized and could be considered as potential drug candidates for the treatment of pain and inflammation. The anti-inflammatory properties were investigated for all the synthesized conjugates. Among 14 synthesized conjugates, four (5a, 5b, 5d, and 5e) were found to have significant anti-inflammatory properties potency 117.6%, 116.5%, 93.8%, and 109.1% in comparison to reference drugs ibuprofen (97.2%) and indomethacin (100%) in the rat paw edema carrageenan test without any ulcerogenic liability. The suppression effect of cytokines IL-6, TNF-α, and iNOS in addition to NO in the LPS-induced RAW264.7 cells supports the promising anti-inflammatory properties observed in the ibuprofen conjugates. In addition, several conjugates showed promising peripheral and central analgesic activity. The selectivity index (SI) of compound 5a (23.096) indicates the significant efficacy and selectivity for COX-2 over COX-1. Molecular modeling (docking and QSAR) studies described the observed biological properties.