Introduction Hypertension (HTN) is one of the most common conditions encountered in daily practice in hospitals. Combination therapy is mostly initiated in the management of HTN when target blood pressure is not achieved with monotherapy. There are few studies comparing the antihypertensive effect of a combination of azilsartan and amlodipine with a combination of amlodipine and other angiotensin receptor blockers (ARBs), however, the results are contradictory. The objective of this study was to compare the efficacy and safety of the azilsartan and amlodipine combination versus the telmisartan and amlodipine combination in hypertensive patients. Methods The present study was a prospective, randomized, active-controlled, open-label, parallel-group clinical trial. Hypertensive patients were randomized into two groups of 25 patients each. Baseline evaluations of systolic blood pressure (SBP), diastolic blood pressure (DBP), and high-sensitivity troponin I (hsTnI) were done. Patients were reassessed after 12 weeks of drug therapy with azilsartan 40 mg and amlodipine 5 mg combination or telmisartan 40 mg once daily (QD) and amlodipine 5 mg combination QD. Results The response rate (defined as a reduction of more than 20 mm Hg in SBP or 10 mm Hg in DBP or both from baseline at 12 weeks) for HTN in the test group and control groups was found to be 88% and 96% respectively. The response rate of the azilsartan amlodipine group was found to be non-inferior to the telmisartan amlodipine group (odds ratio, OR, 0.31, p = 0.61) at the end of 12 weeks of drug therapy. At 12 weeks of follow-up, there was a significant decrease in SBP (p < 0.001), DBP (p < 0.001), and hsTnI levels (p < 0.001) in both groups from baseline values. However, differences between the test and control groups for blood pressure and hsTnI were found to be not statistically significant at 12 weeks of follow-up. The most commonly reported adverse effect in both groups was headache. Conclusion Azilsartan amlodipine combination had an 88% response rate, which was non-inferior to the telmisartan and amlodipine combination. Biomarkers such as hsTnI showed a significant decrease in both groups after 12 weeks of follow-up. However, there was no significant difference between the two groups.