Introduction: Abdominal oncologic surgeries pose significant risks due to the complexity of the surgery and patients’ often weakened health, multiple comorbidities, and increased perioperative hazards. Hypotension is a major risk factor for perioperative cardiovascular complications, necessitating individualized management in modern anesthesiology. Aim: This study aimed to determine the dynamics of changes in troponin and NTproBNP levels during the first two postoperative days in patients undergoing major cancer abdominal surgery with advanced hemodynamic monitoring including The AcumenTM Hypotension Prediction Index software (HPI) (Edwards Lifesciences, Irvine, CA, USA) and their association with the occurrence of postoperative cardiovascular complications. Methods: A prospective study was conducted, including 50 patients scheduled for abdominal cancer surgery who, due to the overall risk of perioperative complications (ASA class 3 or 4), were monitored using the HPI software. Hypotension was qualified as at least one ≥ 1 min episode of a MAP < 65 mm Hg. Preoperatively and 24 and 48 h after the procedure, the levels of NTproBNP and troponin were measured, and an ECG was performed. Results: We analyzed data from 46 patients and found that 82% experienced at least one episode of low blood pressure (MAP < 65 mmHg). However, the quality indices of hypotension were low, with a median time-weighted average MAP < 65 mmHg of 0.085 (0.03–0.19) mmHg and a median of 2 (2–1.17) minutes spent below MAP < 65 mmHg. Although the incidence of perioperative myocardial injury was 10%, there was no evidence to suggest a relationship with hypotension. Acute kidney injury was seen in 23.9% of patients, and it was significantly associated with a number of episodes of MAP < 50 mmHg. Levels of NTproBNP were significantly higher on the first postoperative day compared to preoperative values (285.8 [IQR: 679.8] vs. 183.9 [IQR: 428.1] pg/mL, p < 0.001). However, they decreased on the second day (276.65 [IQR: 609.4] pg/mL, p = 0.154). The dynamics of NTproBNP were similar for patients with and without heart failure, although those with heart failure had significantly higher preoperative concentrations (435.9 [IQR: 711.15] vs. 87 [IQR: 232.2] pg/mL, p < 0.001). Patients undergoing laparoscopic surgery showed a statistically significant increase in NTproBNP. Conclusions: This study suggests that advanced HPI monitoring in abdominal cancer surgery effectively minimizes intraoperative hypotension with no significant NTproBNP or troponin perioperative dynamics, irrespective of preoperative heart failure.