An early brace from Scott McTominay coupled with first half strikes from Bruno Fernandes and Victor Lindelof ensured a dominant three points for Solskjaer.
Leeds have established a reputation as fast starters this season, but the tables were turned in Manchester as McTominay smashed home twice inside the first five minutes.
With Leeds still settling into the surroundings they cheaply lost the ball in midfield, Fernandes slipped in McTominay and he arrowed one past Illan Meslier.
And with the confidence soaring through him, McTominay repeated the trick two minutes later as he latched onto Anthony Martial’s pass to make it 2-0.
United then simply laid siege to Leeds’ goal before the break as Fernandes swept home a loose ball and Lindelof sharply fired home from a corner.
Leeds skipper Liam Cooper did nod home a glimmer of hope for Marcelo Bielsa before the break, but it was a mountain to climb in the second half.
But any team built by Bielsa will always fight back against the odds and David De Gea was forced to make a point blank stop from Raphinha on 56 minutes.
And any slim chance of a dramatic turnaround was ended by the hosts with 25 to play as Dan James netted his first of the season.
McTominay turned provider this time round, with a driving run and ball into the Welshman, who confidently tucked away past Meslier.
But the rampant hosts were not finished there as Fernandes tucked home from the spot for six before Stuart Dallas smacked home another consolation.
United did almost match Liverpool’s seven goals from yesterday, as Meslier denied Edinson Cavani late on, but in the end Solskjaer was forced to settle for a sexy six.
Full Time at Old Trafford it’s Manchester United 6 Leeds United 2