Chelsea captain Millie Bright said during the build-up that they had to take their emotions out of the tie having suffered enough heartache against Barcelona in the past.
In a lively encounter, the visitors did well initially to limit Barcelona's chances and Hampton was tough to beat in a resilient first half.
However, all of that work went out the window in a devastating final 20 minutes as Barcelona showed why they have dominated European football in recent years.
With Chelsea tiring and pushing for an equaliser, Barcelona demonstrated their ruthless streak, piling on the pressure to build a comfortable lead.
That has caused huge damage to manager Bompastor's chances of guiding Chelsea to their first Women's Champions League title in her first season after replacing Emma Hayes.
And it has also threatened to end their hopes of securing a quadruple this season.
It means Chelsea will have to produce one of their greatest performances in the second leg to stand a chance of reaching the final.
Barcelona, meanwhile, are in a strong position to continue their push for a third successive Champions League trophy.
There were spells of Chelsea's performance that showed they could compete but they were not good enough across the 90 minutes and may have paid a heavy price.