But Leicester were level as Bruno Fernandes – who set up Rashford’s opener – lost possession deep inside his own half, with Harvey Barnes then capitalising on sloppy pressing from Scott McTominay to catch David de Gea flat-footed with a strong drive from outside the area.
After the break, Rashford missed another big opportunity as Kasper Schmeichel made a strong stop in a one-on-one battle, while Anthony Martial had the ball in the net but was given offside following a VAR review.
With United in the ascendancy, Solskjaer brought on Edinson Cavani – and the Uruguayan forward played in Fernandes with a killer through-ball for the Portuguese to finish with 11 minutes remaining.
The visitors’ defence had kept Jamie Vardy quiet for long periods, but the Foxes forward punished slack marking to pounce on a cross and send the ball in via Axel Tuanzebe to seal a point for Leicester.
The result ensures Leicester remain a point above United in second place, though leaders Liverpool aeguably benefit more from the draw than either side at the King Power.
Following the match, Solskjaer told BT Sport: “We’re disappointed that we didn’t win because we had loads of big chances and could have finished it off,” Solskjaer told BT Sport.
“Both (Leicester) goals should have been closed down quicker. First one, definitely, and the second one down the side we should have stopped the cross.”
United defender Victor Lindelof was forced off in the second half with a back injury and Solskjaer said: “He’s struggled with his back. He’s struggled for a little while and we might have to do something. Let’s see what it is.”
This weekend get a £10 free bet with Betfair, when you bet £10 on a Same Game Multi on the Premier League.
Terms: Min £10 Same Game Multi bet on any EPL match this Fri- Sun. Free bet valid for 72 hours, awarded at bet settlement. Excludes cashed out bets. T&Cs apply.