One of the greatest threats to human health in modern times and a significant global health concern is antibiotic resistance. The combination of the carbapenemase inhibitor ceftazidime with tebipenem may be of high benefit for fighting resistant bacteria. By using a rapid and extremely sensitive HPLC-UV technique, the simultaneous estimation of ceftazidime and tebipenem in rats was possible. Acetonitrile was used in the protein precipitation procedure to prepare the samples. The best chromatographic conditions were established by applying C18 INERTSIL ODS-3 column with a mixture including 0.05 M phosphate buffer pH 4.2 modified with 85% ortho-phosphoric acid: acetonitrile (70:30, v/v) as a mobile phase at a flow rate 1 mL/min at 25◦C. The ceftazidime, tebipenem, and doripenem as internal standard were maintained at approximately 5.52, 7.31, and 9.90 min, respectively. The bioanalytical technique has been validated according to the European Medicines Agency guidelines. The calibration graphs for ceftazidime and tebipenem were created from 1–40 µg/mL and 0.5–30 µg/mL with R2 = 0.9999 and 0.9994, respectively. The technique was effective in an in vivo pharmacokinetic investigation where rats were given oral and intraperitoneal doses of tebipenem and ceftazidime, respectively, and their plasma levels were measured. Upon the pharmacokinetic parameter calculations, a statistical analysis was carried out. In addition, greenness, whiteness, and blueness assessments of the developed method were conducted and it was approved as an environmentally benign method. The Blue Applicability Grade Index, a novel metric instrument, is introduced to evaluate the applicability of the established approach, and it is given a 77.5 score. Besides, the Analytical Greenness metric and red-green-blue paradigm have been estimated; it has achieved a great score of 0.58 and 85.3, respectively. These developed method’s scores have finally been compared to those of previously published methods.