PAUL POGBA struck two more goals as Ole Gunnar Solskjaer wrote his name into Manchester United history.
Matt Busby and Jose Mourinho are the only United managers to have won their first three matches in charge.
But Solskjaer now joins that list and with games against Newcastle and Reading in the next week he will be confident of extending his run.
Pogba took his tally for the Christmas period to four goals – and could easily have had a hat-trick in another man-of-the-match display.
United were ahead within five minutes as some great work by Marcus Rashford on the right wing saw him go past two defenders and cross for Pogba to bundle home.
Bournemouth could have levelled when Nathan Ake’s header struck Ander Herrera then hit the shoulder of David De Gea and stayed out.
But just after the half hour, United doubled their lead when Ashley Young laid the ball off for Herrera whose cross from the right was nodded in by Pogba at the front post.
And shortly before the break it was three as Anthony Martial clipped over a cross with the outside of his foot and Rashford volleyed home from close range.
The Cherries did get one back when David Brooks found space in the area and centred for Ake to nod home.
It gave the visitors – who have lost eight of their last 10 before this – a glimmer of hope of a comeback.