United's run of form has seen them be unbeaten in 11 games in all, with two wins coming in the FA Cup, only failing to beat Burnley but even that game didn't halt their momentum as they came from 2-0 down to draw 2-2 in a result that must have felt nearly like a win.
Their next Premier League game is a huge one against title challengers Liverpool at Old Trafford on February 24 but before then face PSG in the Champions League and a trip to Chelsea in the FA Cup.
United have won nine and drawn one of 10 matches in all competitions under Solskjaer, while a renewed focus on attacking football has allowed players such as Paul Pogba and Marcus Rashford to flourish.
Pogba was again influential for United, scoring the first and adding the third from the penalty spot in the second half to make the game safe.
Playing with a four-man backline, Ranieri's men held tight until United deviated from the script for the first time in the 14th minute.
Pogba smashed home the opener after Martial's delicate pass into the box, as the Frenchman dominated early proceedings from central midfield.
"I just spoke to him outside here".
Chambers and Aleksandar Mitrovic had chances during a rare Fulham period in the ascendancy, with Ryan Babel somehow hitting the post from close range after substitutes Alexis Sanchez and Scott McTominay went close at the other end.
"Of course I look at the squad, players, who can produce and perform now, next year and in two years?"
United, by contrast, remain unbeaten under Solskjaer ahead of matches against PSG, Chelsea and Liverpool.
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Robert Whittaker & Kelvin Gastelum's UFC 234 Staredown
It's obviously a huge blow to Whittaker, 28, who was forced to pull out of a title defense on home soil in February 2018. In a later statement, UFC said Whittaker had undergone emergency surgery due to a "severe abdominal injury".
Second North Korea summit will be in Hanoi, Trump says
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House Democrats take first step to access Trump tax returns
Republicans are prepared to say that Neal's request is a political witch hunt, rather than legitimate government oversight. Watch:As lawmakers begin to hash out border security, how do conference committees work? "Let's see what happens".