Hilda's crossing of western Cuba slightly disrupted the intensification of the tropical cyclone, but strengthening resumed shortly thereafter. Upon reaching the Gulf of Mexico later of September 29, Hilda began to track very slowly at an average speed of , later meeting the threshold of hurricane intensity at 1200 UTC on September 30. During that time, atmospheric conditions over the Gulf of Mexico rapidly improved; a preexisting belt of strong wind shear, which would have inhibited further cyclonic strengthening, disintegrated coincident with Hilda's passage of the gulf. Rapid intensification ensued on October 1, and by 0600 UTC that day Hilda became a major hurricane. Twelve hours later, the hurricane reached its peak intensity with maximum sustained winds of 150 mph (240 km/h) and a minimum barometric pressure of 941 mbar (hPa; 27.79 inHg) based on reconnaissance flights. During this phase the storm was centered roughly south of New Orleans, Louisiana. Around the same time, an abnormally strong trough centered over Mississippi began to sharply curve the forward motion of Hilda towards the north.