Klebsiella pneumoniae is a global health threat and bacteriophages are a potential solution in combating pandrug-resistant K. pneumoniae infections. Two lytic phages, LASTA and SJM3, active against several pandrug-resistant, nosocomial strains of K. pneumoniae were isolated and characterized. Their host range is narrow and latent period is particularly long; however, their lysogenic nature was refuted using both bioinformatic and experimental approaches. Genome sequence analysis clustered them with only two other phages into the new genus Lastavirus. Genomes of LASTA and SJM3 differ in only 13 base pairs, mainly located in tail fiber genes. Individual phages, as well as their cocktail, demonstrated significant bacterial reduction capacity in a time-dependent manner, yielding up to 4 log reduction against planktonic, and up to 2.59 log on biofilm-embedded, cells. Bacteria emerging from the contact with the phages developed resistance and achieved numbers comparable to the growth control after 24 h. The resistance to the phage seems to be of a transient nature and varies significantly between the two phages, as resistance to LASTA remained constant while resensitization to SJM3 was more prominent. Albeit with very few differences, SJM3 performed better than LASTA overall; however, more investigation is needed in order to consider them for therapeutic application.