Rashford scored his first goal of season for United as the young striker converted Henrikh Mkhitaryan's corner three minutes after coming on.
Manchester United head into the global break having won all three of their Premier League games, achieving clean sheets in each one.
Manchester United's flawless start to the 2017-18 Premier League season continued on Saturday, as the Red Devils beat Leicester City 2-0 at Old Trafford.More news: Jose wants Man Utd to Sign Riyad Mahrez
"It's tough competition with very good players".
Goalkeeper Kasper Schmeichel was the hero for the Foxes in the first half and saved a penalty from Romelu Lukaku early in the second, but there was nothing he could do about Marcus Rashford's strike in the 70th minute.
"After missing the penalty team remained confident and we deserved it".
And like last week at Swansea, Mourinho's subs made the difference, scoring two vital goals to ensure that the Red Devils will go into the global break at the top of the Premier League table.More news: Spend more on aid in Afghanistan
United were unable to make a first-half breakthrough despite being on top, Juan Mata having a goal disallowed for offside shortly before drawing a stunning save from Schmeichel.
"It has been good - getting to know the club, everything around, all the players, the leaders and the system". United heads into the global break with a spotless 3-0 record. "They are on the bench waiting for a chance". If I don't have them on the bench, I can not make successful changes. If i have to choose a word to describe my team, I would have to say "solid". I watched the match many times.
According to the British media, Jose Mourinho was against this transfer until last week, however, his close relationship with Peter Lim has seen a shift in stance where the United manager is now in agreement to send the player out on loan for rest of the season.More news: Instagram alerts high-profile users their data may have been accessed
- Eric Schmidt reportedly pressured think tank into firing Google critic
- Kevin Hart, Chris Young donate to Hurricane Harvey relief efforts
- Potential Tropical Storm Irma
- Christie had 'extensive' talk with Trump on controversial Arpaio pardon
- Kid Rock to Open Restaurant at Little Caesars Arena in downtown Detroit
- Solon recalls Imelda story on Marcoses' 7000 tons of gold
- President Trump goes to Texas Tuesday
- Barnes & Noble Education shares drop as first-quarter earnings miss expectations
- How to donate to Hurricane Harvey victims (and avoid a scam)
- Trump team chooses Springfield visit for symbolic, tactical reasons