In fact, the Red Devils could end the week in the top four, should Chelsea fail to win against Manchester City on Sunday.
And they were made to pay for their profligacy when Pogba gave United the lead on 14 minutes.
Craven Cottage, normally such a genteel place to watch a game of football, was an angry place with fans aiming chants of "You don't know what you're doing" at a manager who appears to have run out of ideas after three months in the job.
Fulham vs Manchester United gets underway at lunch time, kicking off in west London at 12:30pm at Craven Cottage.
United substitute Alexis Sanchez shot straight at Rico when clean through and then saw his cross nodded just over by Scott McTominay, while Fulham's best chance for a consolation goal fell to Ryan Babel, who somehow hit the outside of the post from practically on the goal-line, drawing a wry smile from his manager. From there it was game over for Fulham, who remain firmly rooted in the relegation zone.
It is an 11th league game without defeat against Fulham and marks the first time they have won six matches away from home in a row since May 2009.
Solskjaer said that while there was a chance his tinkering could have backfired, his footballing philosophy was "if you don't risk, you don't win". It was a clinical, sometimes classy display from the Frenchman.
But that confident play was short-lived, with an early error by Fulham centre-back Maxime Le Marchand sapping confidence. "There are big games coming up and that will decide where we are going to finish at the end of the season".
- Martial has now been directly involved in 50 Premier League goals (33 goals, 17 assists) - more than any other United player since his debut in September 2015.