Developing sustainability competence requires engineering graduates to weigh precision against cost, energy demand and regulatory limits, yet calculus instruction rewards exactness as the only correct answer, leaving students reluctant to settle for an adequate, resource-efficient solution. This study proposes the DRAP model (Dual-track Reasoning—Rigour-anchored Standard Operating Procedure (SOP)—Applied Practice—Post-practice Review), integrating the key competencies for sustainability framework, threshold concept theory and boundary management, and delivers it through a five-act chemical oxygen demand (COD) monitoring case. A quasi-experimental study was conducted with 114 first-year environmental engineering undergraduates (experimental n = 57; control n = 57; four intact classes delivered as two combined teaching units, one per condition). The primary outcome was the quality of the decision record produced in a worksheet format, covering boundary identification, decision compliance, cost–precision trade-off and risk anticipation and rated independently by three of the course’s teachers on anonymised submissions; class-level response entropy and individual-level integration choice described how reasoning was distributed. After controlling for pre-test cognitive state, the experimental group showed higher odds of selecting dual-track integration (OR = 3.57, 95% CI [1.38, 9.22], p = 0.017); SOP scores were higher (M = 79.83 vs. 66.17, p < 0.001, d = 0.97); and the difference between the two units persisted after controlling for baseline mathematical proficiency (partial η² = 0.24–0.30), most strongly on the cost–precision trade-off among the four dimensions. Embedding resource-efficiency and compliance constraints as decision premises within mathematical approximation offers a course-level route to the competences that SDG 4.7 and SDG 12 set out, without additional contact hours.