The main historical and architectural landmark of Nevezhkino is the stone church, which is in a ruined state. It was founded in 1811 with funds from parishioners to replace the burned wooden temple, and in 1819, the priest Vasily Fyodorov from Atkarsk consecrated the new building in the name of the unmercenaries Cosmas and Damian. There was a watchman's lodge by the church, and the territory was fenced with a wooden fence. The church building was made of stone with a wooden dome, and a stone bell tower was added in 1873. The clergy consisted of a priest and a psalmist, for whom church houses were provided. The parish included not only Orthodox Christians but also Catholics, Lutherans, Spasovtsy, and Old Believers of the Austrian type, and it included the village of Shmakova Balka.

With the arrival of Soviet power in 1931, the church was closed, and its rector, priest Alexander Perov, was repressed. The reconstructed building later housed a village club. After a fire in 1994, the building remained empty for a long time, and its restoration only began after the revival of the Nevezhkino Orthodox parish in 2013. Now, thanks to the efforts of volunteers, the church premises have been cleared of construction debris and are awaiting major restoration.