THREE goals in 10 minutes at the start of the second half carried Chelsea off to the Amsterdam ArenA on a tidal wave of euphoria.
Ahead 2-1 from the first leg and in danger of slipping into complacency, they were reminded that the job was not quite done when Mohamed Salah scored for the Swiss.
But the shock of that strike with the last kick of the first half served to galvanise the Blues, who can look forward to their second Euro final in two years.
They will play Benfica in the Dutch capital on May 15, a side they beat on their way to winning the Champions League last year.
Fernando Torres, who has enjoyed himself in this competition, got a goal to level it on the night before Victor Moses and David Luiz (pictured) cashed in on a purple patch.
The Brazilian's goal was a glorious curling shot from outside the area that settled the argument before the hour was up.
Chelsea now also have the chance to join a select band of clubs to have won all the major European competitions – an achievement which ought to go some way towards making up for all the other bits of silverware that have slipped through their fingers this season.
Buoyant Chelsea fans, who repeatedly sang the name of Jose Mourinho, who most would love to see return, had none of the tension they have had to endure in past Champions League semi-finals, so comfortable was the winning margin.
It all ended well, but the Blues were sloppy in the first half and fortunate Marco Streller did not connect properly with an early chance.
The Basel skipper connected much better in the 25 th minute, causing a sharper intake of breath from fans at the Matthew Harding end.
The Blues did most of the pressing and were soon creating chances themselves. A Torres chip found Frank Lampard lurking behind the last defender inside the area and the midfielder's shot came back off a post.
Ten minutes later, and Torres clipped a low shot from the edge of the area that keeper Yann Sommer scrambled to get down to and turn aside for a corner.
The Blues went even closer after half an hour when Eden Hazard and Moses combined near the left byline to set up Ramires for a clear chance, even though he had defenders in attendance.
The Brazilian's low strike was just about kept out by Sommer, who was anxious to atone for his disappointing last minute blunder in the first leg that allowed David Luiz's free-kick to beat him.
Basel kept piling forward at every opportunity, making it compelling viewing. They had a shout for a penalty following a possible handball during a goalmouth scramble before Fabian Schar drilled wide and on the stroke of half time, Valentin Stocker slipped a clever ball through for Salah to curl calmly past Petr Cech.
It served as a wake-up call, with Torres equalising four minutes into the second half. The Spaniard was on hand to fire into the roof of the net after Sommer could only palm a low left footer from Lampard in front of him.
Three minutes later and home smiles widened when a blocked shot from Torres fell kindly for Moses and although a defender got in the way of the ex-Palace man's first effort, the ball stayed at his feet and he swept home.
Just before the hour, it was game over when David Luiz hit a sumptuous left footer from outside the area that left Sommer static.
Lampard, still seeking the goal that will take him to 202 goals for the club to equal Bobby Tambling's record, had unselfishly laid the ball into space.
Basel were not quite on their knees and struck the woodwork in one raid, but for them, the damage had been well and truly done.
Line up: Cech; Azpilicueta, Cahill, Ivanovic, Bertrand; Lampard, David Luiz (Ake 82); Ramires (Oscar 66) Hazard (Mata 75), Moses; Torres. Subs not used: Turnbull, Ferreira, Terry, Benayou.