The Norwegian coach has enjoyed almost undiluted success since replacing Jose Mourinho as Red Devils boss, with one home draw against Burnley the only blemish on his domestic winning streak.
Even without the injured Neymar, PSG had too much for the three-time European champions, as goals from Presnel Kimpembe and Kylian Mbappe left United with a mountain to climb upon their return to the Parc des Princes.
Paul Pogba has been a player reborn under Solskjaer, finally revealing the immense qualities that were largely absent under Mourinho.
However, he too endured an evening to forget against PSG, seeing red in the 89th minute to further compound United’s misery.
Indeed, in this context, it’s easy to see why both Solskjaer and Pogba will have been desperate for cup progress when they faced old foe Chelsea on Monday evening.
In the end, the pressure dissipated pretty quickly, with Ander Herrera putting the visitors 1-0 up just after the hour mark.
Pogba added another just before half time—diving between Cesar Azpilicueta and Antonio Rudiger to meet a Marcus Rashford cross—to put the contest past a beleaguered Chelsea.
Just as the verve and vitality of this United team had put Arsenal to the sword in the previous round, undermining the optimism of a new regime and exposing Unai Emery’s approach, so they proved too much for Maurizio Sarri’s Chelsea here.
The Italian coach, who stubbornly sticks to a tactical approach that simply isn’t working, and who continues to run through the most predictable rotation of in-game changes and personnel tweaks, may have reached the end of the road here.
He maintained his place in the dugout despite the 4-0 rout by Bournemouth or the capitulation at Manchester City, but little is improving and his team appear no closer to getting on board with the coach’s idiosyncratic approach.
Only Eden Hazard, a typically lively and inventive presence down Chelsea’s left, could hold his head high after a weary and uninspired team display.
Yet while Sarri runs out of ideas, Solskjaer continues to galvanise this United side, who showed few ill effects of their midweek troubles against PSG.
Rashford and Herrera have come on leaps and bounds under the new coach, while Pogba continues to deliver the kind of performances that might begin to justify his eye-watering transfer fee!
Against Chelsea, he was immense, assisting Herrera for the opener before adding his own goal less than 15 minutes later.
No United player created more goalscoring opportunities or completed more dribbles than Pogba, and it was his excellence that forced the issue in a game that had been cagey up to that point.
The midfield powerhouse is clearly enjoying his football again under Solskjaer, and with the PSG blip looking to be behind them, the Red Devils appear set to end the season strongly.
Could the Norwegian boss guide United to a record-equalling 13th FA Cup?