An own goal gave Barca the lead in the first minute, and Alexia Putellas, Aitana Bonmati and Caroline Graham Hansen also got on the scoresheet in the first half.
It’s a final pitting organisations made famous over decades by men’s teams but now enjoying the rewards of greater investment in the women’s game.
Liverpool beat arch-rivals Manchester United 4-2 to give their Champions League hopes a huge boost after fan protests at United’s home ground continued.
City beat PSG 2-1 at the Etihad Stadium and will face the winner of the other semi-final between Chelsea and Real Madrid.
Second-placed Manchester United remain on target to qualify for the competition they tried so spectacularly to leave.
Manchester United have beaten Tottenham 3-1, strengthening their grip on second place in the Premier League and dealing a further blow to former manager Jose Mourinho’s Champions League hopes.
An argument over a red card led to players from both Paris St Germain and Istanbul Basaksehir leaving the field mid-match in December.
Victory dragged Tottenham back into the Champions League race with Jose Mourinho’s eighth-placed side on 42 points from 26 matches, while Everton beat West Brom 1-0.
Ryan McGowan has been in Scotland with family since winning the A-League grand final and was training with his old club Hearts.
Schalke’s struggles in the resumed Bundesliga continued after a 3-0 home defeat to Augsburg left them 16 points off the Champions League spots.