However, aside from a Matty James shot which went harmlessly wide, the Foxes failed to make the most of the ball and they should have been made to pay in the 18th minute when Juan Mata netted from close range, only for the assistant to rule the Spaniard offside when he appeared to be level.
But just three minutes after coming, substitute Rashford opened the scoring by volleying home a corner in the 70th minute.
After back to back 4-0 wins over West Ham and Swansea, United have maximum points in the EPL without having conceded a goal. They walked off having had almost 70 percent possession and 14 attempts of goal with Paul Pogba, freed to go forward with the insurance of Nemanja Matic behind him, had six on his own.
Last season the French winger came under some criticism and found himself on the bench for parts of the season under Jose Mourinho.
Speaking at his pre-match media conference ahead of Manchester United's clash against Leicester City at Old Trafford on Saturday evening, Mourinho discussed his transfer plans in the remaining days of the summer transfer window.
After a poor performance against Real Madrid in the UEFA Super Cup, Lindelof has been left out of United's Premier League side for their first three games, failing to even make the substitutes' bench on two of those occasions. He'd only been on the pitch three minutes.
It may be that Martial and Rashford are locked in a battle to start all season.
Ibrahimovic has been recovering from a serious knee injury that cut short a stellar 28-goal first season at Old Trafford and Mourinho says he is looking forward to unleashing him in the second half of the campaign.
"But I am happy if I am not going to have that and I don't think I am going to have that", Mourinho said.
Leicester's form didn't pick up until Craig Shakespeare took over from Claudio Ranieri in February, and the reigning champions began to climb away from the relegation places.