Danny Graham handed Blackburn the lead against the run of play after 17 minutes but Marcus Rashford‘s calm finish ten minutes later restored parity before half time.
Ibrahimovic was then thrown into the fray with 28 minutes remaining and combined brilliantly with Paul Pogba to power home his 24th goal of the season.
And the Swede, speaking after the game, made it clear that Mourinho’s men are very much behind the Portuguese’s methods.
“I think the team did well before we came on and we’re unlucky with the goal,” he said. “Me and Paul came in to boost that a little.
“We are still in every tournament let’s say and we keep working hard and gaining confidence.
“Every game is unpredictable in England, it’s back and forth. The least mistakes possible wins the game.
“We believe in what we are doing.”
This felt like a genuine cup tie away from home: an old, historic ground, the rain pouring down, and Man United surging forward – their fans occupying an entire stand – in search of a winner, launching a relentless stream of attacks until, finally, their supreme talisman stood up once again to book his side a place in the quarter final.
Nobody can doubt that, for the first time since Robin van Persie‘s opening campaign at Old Trafford, United pose a genuine threat up-front under Mourinho. Players like Zlatan bring a certain presence to any game, almost as if they can alter the atmosphere’s overall frequency, and as the Swede and Pogba limbered up to come on you could almost smell the change of tone at Ewood Park. Mourinho was introducing the big guns, and they duly decided the encounter within minutes of coming on.