The Blues travelled to West Yorkshire with 6,000 miles already clocked up over recent days following their return from Club World Cup duty in Japan, and it looked as though that weariness would cost them when Luciano Becchio gave the Championship side a first-half lead.
But Chelsea found a second wind after the break, with Ivanovic one of five different scorers as Rafael Benitez's men booked a semi-final date with Swansea.
It was a resounding way for the European champions to respond to their Club World Cup final loss on Sunday but, according to Ivanovic, they were worried it would not turn out that way.
"Leeds was a very difficult game which came at a very difficult moment for us. We didn't have a lot of time to adapt," he said.
"We were tired and that is why it was a little scary for us at the beginning. We didn't know how we were going to feel at the start of the game, but now we have to look forward.
"We have to recover well because we still feel the strain from Japan and we will probably still be adapting a week after coming back."
Ivanovic was joined on the scoresheet by Juan Mata, Victor Moses, Eden Hazard and Fernando Torres as Leeds, old and bitter rivals of Chelsea, were put to bed.
A two-legged tie with Swansea was then served up and Chelsea are the near-unbackable favourites to win a competition which sees Aston Villa and Bradford drawn together in the other semi-final.
According to Ivanovic, though, having already spurned the chance to win the Community Shield, Champions League and Club World Cup this season, Chelsea have to take everything seriously from here on in.
"Swansea is a different team to other ones, they like to play," he added.
"We are at home in the first leg so we know we have to be on top of them and try to get a good result to make the final.
"This is our chance. We have gone far in this competition, we have to be ready and do everything to win it.
"We have missed out on three trophies this season and don't want to make it a fourth. But we shouldn't think any more about that, you have to deserve to win them."
The defeat to Corinthians in Yokohama inevitably made waves with regard to the direction Chelsea are going in, and Ivanovic knows how important last night's win was as a result.
"I think it was very important for us to show a reaction after the disappointment of what happened in Sunday's game. But this is just one game," he said.
"We have to be more focused and stay like that in every game and try to win the next couple of matches. It is only winning game-by-game that we can get back our mentality and be strong like we were before."