Pogba had gone five games without scoring following his £89 million ($115 million, 102 million euros) arrival from Juventus and had to endure criticism of some below-par performances.
But the 23-year-old France midfielder was on the scoresheet at last in the 42nd minute at Old Trafford.
Timing his run perfectly, Pogba met Daley Blind's corner with a powerful header that gave Leicester goalkeeper Ron-Robert Zieler no chance.
It was United's fourth goal of the half as Jose Mourinho's side demolished the Premier League champions.
"I am very happy for the result and the goal. I hope that is not going to be the last," Pogba told Sky Sports.
Pogba's goal was just one of many encouraging aspects of United's display as they got back on track following two successive league defeat.
Asked if he was bothered by criticism of himself and the rest of the United squad, Pogba added: "I never look at the newspapers. I say one thing - it is at the end, at the end we will see.
"We were very focused, we knew it was gong to be difficult and we showed a very big performance today. We want to keep on with that."