It took only 31 seconds for Joao Pedro's goal to bring the visitors' new era to life, but despite an attacking display that was scintillating at times, plenty still remained of the defensive frailties that have undermined this team in the recent past.
Robert Sanchez's hopeless attempt to keep out Josh King's first-half equaliser was a reminder of areas of the pitch where Chelsea remain weak despite spending around £350 million ($A667m) this summer.
That outlay included a record £117m ($A223m) lavished on Morgan Rogers. The England forward enjoyed an encouraging debut capped with a slotted finish to make it 2-1 before the break, then Cole Palmer, arguably Chelsea's best player on the night, began the second half with a beautiful finish to make it three.
Had Alonso had longer to work with his defence, Chelsea might have made lighter work of shutting the game down. Instead, they invited Fulham on, Sanchez fumbled again and Gonzalo Garcia nodded in.
There was plenty here to encourage new boss Alvaro Arbeloa, though not every side he faces will be as defensively accommodating as Chelsea.
It had looked like being a long night. In the first minute, Jorge Cuenca's ball out of defence was headed back by Levi Colwill and allowed to run into the path of Palmer. His clipped pass found the run of Joao Pedro who finished stylishly as Bernt Leno advanced.
Chelsea looked nervous defensively, no-one more so than the goalkeeper. Sanchez almost made a mess of turning King's drive behind with a fumbled parry, but the next effort from the Fulham forward flummoxed him completely. Sanchez left too much room at his near post and was slow to get down, King's shot zipping between his flaccid wrists and in.
Joao Pedro volleyed a foot wide from Palmer's cross, Reece James drilled straight at Leno after Rogers's shot was blocked, then Leno deflected Romeo Lavia's close-range effort behind.
Chelsea re-took the lead before half-time and again Palmer was the architect. His neat ball down the right fed the onrushing Maxence Lacroix up from the back, and the defender drew the goalkeeper before picking out Rogers who slotted in.
Palmer had already showed sublime skill to beat four defenders and curl wide when, early in the second half, he made it three. Joao Pedro held up the ball inside the box and waited for the England forward to arrive. When he did, it was the simplest task to prod a finish between the legs of Leno.
Fulham were not beaten yet. It was 3-2 when Timothy Castagne beat Colwill and drew a save from Sanchez that was pushed straight onto the head of Garcia who bounced it in.
Antonee Robinson missed a glorious chance to complete the comeback when he lobbed wide with Sanchez caught out of his goal, then the goalkeeper partially redeemed himself in keeping out Ryan Sessegnon's fierce hit, as Chelsea hung on.
14°C