Making his 100th appearance for the club, Rashford pounced on Paul Pogba’s chipped through ball before rifling beyond Kasper Schmeichel after just nine minutes.
“I think we started brilliantly,” Solskjaer said.
“Marcus had a great chance from Luke’s cross and finished the ball fantastically when Paul played him through. I told him through Schmeichel’s legs because he opens up but it was a great finish so I can’t complain can I?
A breathless finale saw Leicester repeatedly hurl men forward with David De Gea forced to make a series of crucial saves to preserve the clean sheet.
But after grounding out a ninth win in ten games, United now lie just two points adrift of the Champions League places and Solskjaer was thrilled the target he had placed upon himself when arriving at the club was already with touching distance.
“We put our bodies on the line, there’s a couple of bruised noses, knees and dead legs, but they fought for the three points today,” Solskjaer continued.
“We deserved it in that respect. We didn’t play particularly well, but we defended really well; Eric [Bailly] and Victor [Lindelof] fantastic and David [De Gea] again of course.
“A clean sheet is always a foundation to build on and three points will always give the lads confidence. They are not 100 per cent happy with the performance, which is great because we know we can do better than this.”
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