Messi collected a misplaced pass from Ashley Young to curl it into the bottom corner in the 16th minute.
United were all over the place as another lapse from the away side's defence four minutes later cost them as Messi fired a shot from outside the box, which squirmed under goalkeeper David de Gea who made a rare gaffe.
Philippe Coutinho rounded off the utterly convincing victory for the Catalans by curling into the top corner in the second half.
Reaching the last-four stage for the first time since 1996/97, Ajax's 19-year-old captain Matthijs de Ligt headed the winner from the corner in the 67th minute of the quarter-final second leg as the Dutch side came from behind to clinch a 3-2 aggregate win.
Cristiano Ronaldo, aiming for a fourth consecutive Champions League title after winning the last three with Real Madrid, gave Juventus the lead ahead in the 28th minute with an emphatic header, his sixth goal of the competition.
But Donny van de Beek levelled six minutes later before the visitors swept Juventus aside in the second half.
Can we can go on to win the competition? Well, we are in the semi-finals now. And we have eliminated two of the favourites in the last two rounds. The next games will be very difficult, but so were these ones. So who knows?," said De Ligt after the game.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)