The sustainable productivity of rice–wheat cropping systems relies on soil health, and soil health can be positively influenced by treating previous crop residues using conservation tillage practices. The present study examined the impact of three rice residue-management practices under zero-tilled wheat (ZTW) and conventionally tilled wheat (CTW), along with two rice-sowing practices, during rice cultivation on soil functional microbial diversity, physiological profiling, and grain yields of rice and wheat. Anchored residues (ARs) under ZTW exhibited significantly (p ≤ 0.05) high average well color development—31.43% more than CTW with no residue (NR). CTW with residue burning (BUR) showed a 5.42% increase in the Shannon diversity index compared to CTW-NR. Substrate richness was 10.02% higher in CTW-BUR compared to CTW-NR. CTW-BUR demonstrated the highest 17.98% increase in the Shannon evenness index compared to CTW-NR. The direct-seeded rice (DSR) system generally surpassed puddled transplanted rice (PTR) in most indices, except for the Shannon evenness index values. ZTW-AR exhibited the highest utilization of amino acids, carboxylic acids, and phenolic compounds, while CTW-BUR exhibited the highest utilization of carbohydrates and polymers utilization, and ZTW with no-residue (NR) exhibited the highest utilization of amines. Rice and wheat grain yields were highest with full residue in ZTW and lowest in CTW-NR. PTR supported higher rice yields, while DSR was superior for wheat. These findings highlight the favorable role of residue retention with no tillage during wheat cultivation in the maintenance of soil quality and rice–wheat productivity.