Martial, another United star who felt slighted by Mourinho's acerbic tongue, is back to his best and his 11th goal of the season was the flawless way to celebrate signing a new five contract recently.
In fact, the Red Devils could end the week in the top four, should Chelsea fail to win against Manchester City on Sunday.
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.
The decision to make six changes with Tuesday's Champions League last-16 first leg against Paris St Germain on his mind could have backfired in the capital, but Fulham and their awful defence were no match for the visitors.
Pogba's spot-kick wrapped up United's first sixth straight away win in all competitions - their best run on the road since 2009 - as Fulham floundered again under Claudio Ranieri.
United doubled their lead on 23 minutes when Martial showed shades of Cristiano Ronaldo's famous late victor at Craven Cottage in 2007.
It was Fulham who started the game stronger and should have taken the lead when Luciano Vietto squandered a brilliant chance inside two minutes.
The victory lifts United into the Premier League top four for the first time since the opening weekend of the season - having been 11 points adrift when Solskjaer replaced Jose Mourinho in December. 'He's been a threat in the first 20 minutes like you wouldn't believe.
Pogba smashed home the opener after Martial's delicate pass into the box, as the Frenchman dominated early proceedings from central midfield. It was a superbly-hit effort, although goalkeeper Rico could have done better.
United won possession and Phil Jones found the fleet-footed attacker just inside his own half.
In the second half, Manchester United continued to press and were rewarded with a penalty in the 64th minute.
The visitors were now in complete control against a Fulham side looking more and more likely to find themselves playing Championship football next season.
Thankfully this time United were able to put Fulham to the sword with Pogba central to everything good.