Marcus Rashford had missed a wide-open header but put United ahead in the 23rd minute with a cool finish after being slipped in by Fernandes before Harvey Barnes equalised eight minutes later with a fine shot from the edge of the box.
Rashford had a great chance to put United back in front on the hour but his powerful drive was well saved by the right hand of Kasper Schmeichel.
Two minutes later Anthony Martial had an effort disallowed for offside but the influential Fernandes restored United’s lead in the 79th minute, drilling into the bottom corner after being found inside the area by substitute Edinson Cavani.
Again though, the lead was short-lived as Vardy’s first time shot on the half-turn from a low cross from Ayoze Perez, went in off Tuanzebe and earned a point for the Foxes.
“Disappointed we didn’t win today because we had loads of big chances and we could’ve finished it off but they’re a dangerous side,” said Solskjaer.