DNA polymerases have the venerable task of maintaining genome stability during DNA replication and repair. Errors, nonetheless, occur with error propensities that are polymerase specific. For example, DNA polymerase lambda (pol lambda) generates single-base deletions through template-strand slippage within short repetitive DNA regions much more readily than does the closely related polymerase beta (pol beta). Here we present in silico evidence to help interpret pol lambda's greater tendency for deletion errors than pol beta by its more favorable protein/DNA electrostatic interactions immediately around the extrahelical nucleotide on the template strand. Our molecular dynamics and free energy analyses suggest that pol lambda provides greater stabilization to misaligned DNA than aligned DNA. Our study of several pol lambda mutants of Lys544 (Ala, Phe, Glu) probes the interactions between the extrahelical nucleotide and the adjacent Lys544 to show that the charge of the 544 residue controls stabilization of the DNA misalignment. In addition, we identify other thumb residues (Arg538, Lys521, Arg517, and Arg514) that play coordinating roles in stabilizing pol lambda's interactions with misaligned DNA. Interestingly, their aggregate stabilization effect is more important than that of any one component residue, in contrast to aligned DNA systems, as we determined from mutations of these key residues and energetic analyses. No such comparable network of stabilizing misaligned DNA exists in pol beta. Evolutionary needs for DNA repair on substrates with minimal base-pairing, such as those encountered by pol lambda in the non-homologous end-joining pathway, may have been solved by a greater tolerance to deletion errors. Other base-flipping proteins share similar binding properties and motions for extrahelical nucleotides.