Borrelia burgdorferi, the causative agent of Lyme disease in humans, is exposed to reactive oxygen and nitrogen species (ROS and RNS) in both the tick vector and vertebrate reservoir hosts. B. burgdorferi contains a limited repertoire of canonical oxidative stress response genes, suggesting that novel gene functions may be important for protection of B. burgdorferi against ROS or RNS exposure. Here, we use transposon insertion sequencing (Tn-seq) to conduct an unbiased search for genes involved in resistance to nitric oxide, hydrogen peroxide, and tertiary-butyl hydroperoxide in vitro. The screens identified 66 genes whose disruption resulted in increased susceptibility to at least one of the stressors. These genes include previously characterized mediators of ROS and RNS resistance (including components of the nucleotide excision repair pathway and a subunit of a riboflavin transporter), as well as novel putative resistance candidates. DNA repair mutants were among the most sensitive to RNS in the Tn-seq screen, and survival assays with individual Tn mutants confirmed that the putative ribonuclease BB0839 is involved in resistance to nitric oxide. In contrast, mutants lacking predicted inner membrane proteins or transporters were among the most sensitive to ROS, and the contribution of three such membrane proteins (BB0017, BB0164, and BB0202) to ROS sensitivity was confirmed using individual Tn mutants and complemented strains. Further analysis showed that levels of intracellular manganese are significantly reduced in the Tn::bb0164 mutant, identifying a novel role for BB0164 in B. burgdorferi manganese homeostasis. Infection of C57BL/6 and gp91phox-/- mice with a mini-library of 39 Tn mutants showed that many of the genes identified in the in vitro screens are required for infectivity in mice. Collectively, our data provide insight into how B. burgdorferi responds to ROS and RNS and suggests that this response is relevant to the in vivo success of the organism.