Joe Rindl, BBc Sport
Aston Villa were the better side in the closing stages and could easilyhave booked a spot in the fifth round.
But the match might also have been out of Villa's reach by half-time if Chelsea were to have put away some of their numerous chances.
Villa Goalkeeper Emiliano Martinez, "the world's number one", was in excellent form at Stamford Bridge.
The Argentine denied Chelsea's Noni Madueke and Cole Palmer from close range and also made two fine saves to prevent own goals, keeping out a Luiz header and Alex Moreno's poked clearance after a low cross from Palmer.
"He played amazing today," Villa manager Unai Emery told BBC Sport at full-time.
"He saved us two or three times. And then he was always ready to cover our centre-backs in behind. Emiliano today, we needed him. And really he played like he is - number one."
As for Martinez, he was rallying his teammates after the final whistle, adding to BBC Sport: "We want to give the fans a cup run.
"That's why they come in numbers, they feel connected with the team. I feel the same way with the national team, with Argentina.
"We felt the same way with our fans and we repaid them with titles. I feel something similar here."