United dominated throughout and did craft a few first-half chances, but they were largely frustrated by a dogged Huddersfield defence.
The visitors' resistance was eventually brought to an end when Romelu Lukaku turned in from close range following a fine Juan Mata cross, and Alexis Sanchez wrapped things up by burying a rebound after his initial penalty had been saved by Jonas Lossl.
Even though United ultimately won comfortably, Mourinho paid tribute to Huddersfield's organisation.
"We always had control of the game, but at half-time it was 0-0," Mourinho told BBC Sport.
"I guess we had around 85 per cent possession in the first half, but it was not enough.
"We kept doing the same in the second and even at 1-0 we were totally in control. Our defensive line was far from the danger areas.
"We had to be patient, but had to keep the intensity high and the pressure. We had to break down the Berlin Wall organised so well by David Wagner."
The victory took Mourinho's side up to 56 points, second in the table and 13 points behind Manchester City.
Meanwhile, the loss dropped Huddersfield Town into the relegation zone for the first time this season.