Background: Pulmonary hypertension (PH) patients are at higher risk of postoperative complications. We analyzed the association of PH with 30-day postoperative pulmonary complications (PPCs). Methods: A single-center propensity score overlap weighting (OW) retrospective cohort study was conducted on 164 patients with a mean pulmonary artery pressure (mPAP) of >20 mmHg within 24 months of undergoing elective inpatient abdominal surgery or endoscopic procedures under general anesthesia and a control cohort (N = 1981). The primary outcome was PPCs, and the secondary outcomes were PPC sub-composites, namely respiratory failure (RF), pneumonia (PNA), aspiration pneumonia/pneumonitis (ASP), pulmonary embolism (PE), length of stay (LOS), and 30-day mortality. Results: PPCs were higher in the PH cohort (29.9% vs. 11.2%, p < 0.001). When sub-composites were analyzed, higher rates of RF (19.3% vs. 6.6%, p < 0.001) and PNA (11.2% vs. 5.7%, p = 0.01) were observed. After OW, PH was still associated with greater PPCs (RR 1.66, 95% CI (1.05–2.71), p = 0.036) and increased LOS (median 8.0 days vs. 4.9 days) but not 30-day mortality. Sub-cohort analysis showed no difference in PPCs between pre- and post-capillary PH patients. Conclusions: After covariate balancing, PH was associated with a higher risk for PPCs and prolonged LOS. This elevated PPC risk should be considered during preoperative risk assessment.