A-TIG welding is a modified form of GTAW process that has become popular due to its ability to create high-quality welded joints with minimal cracks and distortion. This technique is commonly used to join various metals, including stainless steel, aluminum, titanium, and nickel alloys like Hastelloy C-276, which is used in fabrication of complex components across marine, nuclear, aerospace, and chemical industries. In this investigation, A-TIG welding of Hastelloy C-276 was studied using three parameters - welding current, welding speed, and gas flow rate - at three distinct levels. The impact of these parameters were analyzed on two responses, namely penetration depth and width of weld. Macrostructural investigation, sensitivity analysis, and parametric studies revealed that welding current (I) had the most influence, followed by speed of welding (S) and flow rate of gas(G). Full quadratic multiple regression analysis-based models were developed for both responses, which were found to be suitable with a higher coefficient of determination and an average percentage error of 2.165% and 2.624%, respectively. Additionally, a teaching learning based optimization algorithm was integrated with these models to identify the most effective A-TIG parameter combination for higher penetration depth and lower weld width. The MRA-TLBO integrated approach resulted in an optimal parametric combination of I (170A), S (180 mm min−1), and G (11.37 l min−1) that resulted in a penetration depth and weld width of 4.503 mm and 4.684 mm, respectively. Validation at this optimal setting showed an improvement of 3.365% and 1.284% for weld width and penetration depth, respectively, suggesting the robustness of the developed methodology.