Having picked the wrong team, with Paulo Ferriera inexplicably used in midfield, Mourinho watched them go two goals down to John Arne Riise and Luis Garcia and retrieve only one as he belatedly rejigged. Even then Joe Cole, left stewing in the dug-out until the last half-hour, ought to have taken the game into extra-time, hooking a glorious chance into the Stretford End.
But the champions-elect were below their recent best, Frank Lampard failing either to make an impression from his position on the left or subdue his direct opponent, Steven Gerrard. Michael Essien, although declared fit, was again not the force he looked in his first few games for the club, and the formation allowed for no width until Arjen Robben was summoned for the second half, to be followed - as Chelsea went from one extreme to the other - by Cole and Damien Duff.
So Liverpool, for whom the revitalised Harry Kewell demonstrated all the benefits of wing-play, deservedly achieved only a second victory in 10 meetings between the two teams and their antipathetic managers over the past two seasons. At the Millennium Stadium on 13 May, they will meet either Middlesbrough or West Ham, whom they must visit in a rehearsal of sorts on Wednesday.
By the time of the final Chelsea will surely have sewn up a second successive League title, though after losing out again in Europe, Mourinho needed to complete his club's first Double to improve on last season.
Predictably, he refused to admit any misjudgement, concentrating instead on a disallowed goal by John Terry and the gap between the two teams in the Premiership. A final little barb was to wish Liverpool well "in the Champions' League qualifier" - with the emphasis on the word "qualifier".
The use of Ferreira in front of Gérémi looked a dubiously negative tactic from the start, even more so once Chelsea fell behind midway through the first half. Gérémi gave Kewell too much room and Ferreira was not so much a Portuguese man of war as a sardine out of water.
Keeping Didier Drogba and Hernan Crespo together as the attacking pair worked better in the first half, and the Ivorian had two scoring opportunities before Liverpool took the lead. Both were placed wide, the second from seven yards when played clean through. It was a bad miss, punished within two minutes. Terry was adjudged, harshly, to have fouled Garcia and Riise tapped the free-kick square for Gerrard, who merely stopped it, allowing Riise just enough of an angle for his low drive through the end of the wall.
For the rest of the half Liverpool, in their 22nd semi-final, were the more accomplished team. Kewell, switching to the right, found more joy against Asier del Horno, and came inside on to his left foot to drive wide. Terry was lucky to escape with a wayward back-header and in added time, Gerrard set up Garcia, who shot wildly.
Robben, brought on at half-time as the right-footed Ferreira switched to left-back, was quickly involved and thought he had set up an equaliser four minutes into the half with an inswinging free-kick from the right. But Graham Poll infuriated Terry by ruling that Chelsea's captain had leant on Riise at the far post before heading in. Liverpool's second had the most innocuous of beginnings, a throw-in on the right-hand side. Chelsea failed wretchedly to deal with it, Ferreira and then William Gallas heading towards their own goal to allow Garcia a clear run, which he finished with a beautifully placed left-footed drive.
Chelsea sent on Cole and Duff to occupy the flanks, pulling Robben into the centre behind Drogba, which brought about a much-needed improvement. Jose Reina had to save well from Robben, but in the 70th minute Riise headed a cross weakly into the air and Drogba reacted fastest to nod the ball just under the bar. The London support behind that goal came to life at last and the final quarter of an hour was the noisiest of a deafening evening. But after Robben's cross had sat up just as Cole was shooting, Liverpool's thousands sang the loudest, longest and last.