The FA Cup fourth-round victory at Arsenal on Friday took the Norwegian caretaker manager's record to eight successive wins since taking over from Jose Mourinho before Christmas -- a mark that surpasses even the great Matt Busby at the start of an Old Trafford managerial reign.
While it appears Tottenham Hotspur's Mauricio Pochettino remains United’s preferred choice as long-term appointment, the strides Solskjaer is making on and off the pitch make an increasingly compelling case for the 45-year-old to win the job.
A fourth-placed finish, and Champions League football next season, were looking a distant dream in the latter days of Mourinho's reign, but victory over Burnley would lift United level on points with Chelsea, for 24 hours at least.
And if results involving Chelsea and Arsenal were to fall in favour of former United striker Solskjaer -- whose side face a Burnley team looking to recover from a 5-0 FA Cup rout by Manchester City -- the Red Devils could even end the week eyeing a third place currently occupied by Pochettino's Spurs.
Shackles off Pogba
It is all a far cry from the dismal period under Mourinho, with recent results saying much about Solskjaer's man-management skills, as well as his tactics and philosophy.
In his two most impressive wins to date -- a league victory at Spurs and the 3-1 FA Cup defeat of Arsenal -- Solskjaer has opted for a 4-3-3 formation but it has been his choice of personnel that has looked particularly enlightened.
The use of Nemanja Matic and Ander Herrera in midfield has allowed the third member of that group, French World Cup winner Paul Pogba, to take up a more advanced, attack-minded role.
The shackles which Mourinho applied have been removed and Pogba, so often in public dispute with the Portuguese, has arguably benefitted more than anyone from the change in leadership.
Romelu Lukaku, who looked tired and at a not particularly high level of fitness in the final games under Mourinho, also looks a revived figure since Solskjaer returned to Old Trafford.
Against Arsenal, Solskjaer handed the Belgian striker a role wide in the attacking trio, with Alexis Sanchez in the other wide position and Jesse Lingard taking up a central role.
Lukaku, who had been effective from a wide berth at Everton and with Belgium, proved an inspiration against the Gunners.
Meanwhile Sanchez, a major under-achiever since signing for United 12 months ago, turned in one of his best performances for the club, scoring for just the second time this season and the fifth time in total since leaving Arsenal.
In the Spurs victory, Solskjaer had selected the same formation but different personnel, with Marcus Rashford and Anthony Martial supporting Lingard from wide positions.
All of a sudden, a United attack that appeared plodding and one-dimensional under Mourinho looks like one of the most potentially exciting group of forwards in the country, if not across Europe.
But Solskjaer's biggest contribution to the spectacular upturn in fortunes has simply been a matter of philosophy and the attack-first mood he has brought back to Old Trafford.
The Arsenal victory may have been a throwback to former glories in the sense that United were so devastating on the counter-attack.
But after the game United's players spoke, as they have done ever since Solskjaer's arrival, of their new leader's insistence they look to attack and move the ball -- and themselves -- upfield as quickly as possible.
"Since the first day he said we want to be a team that controls the game but sometimes that's impossible," explained Herrera after the Arsenal win.
"Sometimes we have to defend but when we defend we know that anything can happen because we have so many quick, attacking offensive players."