The England international who was marking his 100th cap scored the only goal at the King Power Stadium on Sunday.
Rashford finished clinically from Paul Pogba‘s pass to earn the Red Devils an eighth win in nine Premier League games under caretaker manager Ole Gunnar Solskjaer.
The 21-year-old had headed over within the first five minutes, but soon made amends, controlling Pogba’s pass and placing it beyond the reach of Kasper Schmeichel.
But, United intensity did not match that of recent games and they created little else before half-time, although City also looked devoid of ideas.
The victory over Leicester City has placed United two points behind Maurizio Sarri’s Chelsea who sits fourth.