Greenwood scored late after James Tarkowski had equalised moments after the teen had put the hosts forward within the second half.
It was United’s first dwelling win towards Burnley within the Premier League since February 2015.
“Very pleased with three factors, we have not overwhelmed Burnley right here since 2015. Good outcome, 5 wins on the bounce, that is good kind,” Solskjaer informed Sky Sports activities.
“We have at all times mentioned this yr must be progress and enchancment, we have as many factors as final season after which if we get some extra, we have greater than final season and that is progress.
“We wish to end with a trophy within the Europa League, we have a great deal of video games and masses to deal with.”
Burnley had the ball behind the web after 18 seconds however it was dominated out with the scorer Chris Wooden in an offside place.
Each groups had possibilities to attain earlier than the break with Wooden heading simply broad earlier than Greenwood was unable to get on the top of a Marcus Rashford cross.
The hosts went forward three minutes into the second half when Greenwood fired dwelling from Rashford’s low cross after a intelligent Bruno Fernandes dummy.
Burnley responded lower than two minutes later when Tarkowski scored an equaliser from Ashley Westwood‘s nook.
United had an important probability to retake the lead after 70 minutes however Bailey Peacock-Farrell stopped Fernandes’ header.
The host did return in entrance with six minutes remaining when Greenwood’s deflected strike wrong-footed Peacock-Farrell.
United grabbed a 3rd in stoppage time as substitutes Cavani and Donny van de Beek mixed which noticed the Uruguayan striker rating into an empty internet.
“Very blissful for him,” Solskaer informed the BBC about Greenwood. “He is mixing up his recreation. He goes inside and out of doors, he is maturing on a regular basis.
“It is beautiful to see. He is put the work in on the coaching floor and reaps the rewards.”