Beleaguered Chelsea boss Rafael Benitez earned a little respite as his players defeated Middlesbrough 2-0 at The Riverside.
A day after the manager had moved to play down reports of a rift with skipper John Terry, he saw the England defender lead his side to a place in the last eight where they face a mouth-watering trip to Manchester United.
The Blues took the lead when midfielder Ramires' 51st-minute shot flicked Fernando Torres, who knew little or nothing about it, and flew past keeper Jason Steele before the impressive Victor Moses made sure with a close-range finish 15 minutes from time.
Benitez made no fewer than eight changes to the side which lost 2-0 at Manchester City at the weekend, with only keeper Petr Cech, defender Branislav Ivanovic and midfielder Ramires surviving, and that meant a return for Terry and a first senior start for 18-year-old Dutchman Nathan Ake.
But in the event, Chelsea turned in a tepid first-half display. It took an important block by Nicky Bailey to deny Oscar with 12 minutes gone after Moses had exploded past full-back George Friend and squared for the Brazilian to shoot.
The Blues found themselves having to take a step backwards and might have conceded the opening goal with 26 minutes gone. Striker Scott McDonald met Bailey's driven cross with a powerful header, but saw the ball fly wide of the far post with Cech looking on anxiously.
Mustapha Carayol dragged an ambitious 36th-minute effort well wide, but he forced Cech into a less than convincing save with five minutes of the half remaining when his shot reared up off the turf and hit the keeper in the chest before being bundled to safety.
It took Chelsea only six minutes after the break to break the deadlock. Oscar's determined run to the by-line and floated cross caused problems for the home defence and when Yossi Benayoun fed the loose ball out to Ramires, he curled the ball into the top corner with the help of a slight deflection off the unwitting Torres.
The Spaniard appeared to claim the goal as his team-mates celebrated, but there would have been no question over the shot he unleashed after beating the offside trap had Steele not got his fingertips to it.
Substitute Eden Hazard might have extended his side's lead with a deft shot which just evaded the top corner, but it was he who accepted Oscar's pass seconds later to provide Moses with a tap-in. Cech had to be on his toes to keep out an 82nd-minute free-kick from Merouane Zemmama but Chelsea made it to the final whistle with their clean sheet intact.