With the Premiership defeat at Fulham still ringing in their ears, Chelsea's determination to add the FA Cup to their near certain league title was in evidence from their first worthwhile attack on four minutes.
It was a dream start for the Blues when captain Terry lost his marker Peter Ramage and sliced home a left-footer from eight yards, direct from a Damien Duff corner.
The ball went under the body of goalkeeper Shay Given and deflected into the far corner of the Newcastle goal.
Chelsea had a shout for a penalty two minutes later when Didier Drogba drove the ball into the body of Celestine Babayaro, but referee Steve Bennett waved play on.
Newcastle right-back Stephen Carr had a speculative long-range shot on six minutes, but it went wide of Carlo Cudicini's goal.
Former Chelsea left-back Babayaro was in the action two minutes later, this time foiling Joe Cole by throwing himself in front of the England midfielder's powerful, goalbound drive.
Terry proved what a superb defender he is by denying Alan Shearer from slotting home from four yards after Cudicini parried away a low, left-footed daisy-cutter from Lee Bowyer on 17 minutes.
Noberto Solano saw his fine, curling 25-yard free-kick inch wide of Cudicini's right post on 21 minutes.
This was quickly followed by a fluffed left-footed by Eidur Gudjohnsen, ten yards out, a minute later.
Chelsea should have extended their lead three minutes before the break when incredibly Ricardo Carvalho volleyed a Frank Lampard free-kick wide of the goal with only Given to beat.
Chelsea started the second half in bright fashion with Cole forcing a fine near-post save from Given. The resultant corner saw Asier del Horno flash a volley high and wide.
Drogba got in on the action on 47 minutes, but his weak drive, on target, from just outside the penalty area did not trouble Given.
Cole latched on to an excellent through ball by Claude Makelele and ran into the penalty area, but his cutback cross was belted clear by Robbie Elliott five minutes later.
Under pressure Newcastle replaced left-back Babayaro with Craig Moore on 52 minutes.
However the Australian's first act was to get booked when he kicked into the back of a prone Cole on 57 minutes.
Shola Ameobi was also yellow-carded for a kick and Drogba too for dissent.
A fine counter-attack on 62 minutes saw precise interchange of passes between Gudjohnsen and Duff before the Icelandic striker raced into the Newcastle area, but he pulled his shot across goal instead of towards the net.
In an attempt to seal the game Chelsea boss Jose Mourinho brought on a second striker - Hernan Crespo for Gudjohnsen on 78 minutes - adding Michael Essien to the midfield by replacing an out of sorts Cole.
Shaun Wright-Phillips had already been added to the fray to little effect on 67 minutes.
The change almost worked with six minutes remaining when Wright-Phillips ran 60 yards to latch on to a counter-attacking ball from Lampard, but the wide man blasted over the Newcastle bar from just outside the area.
To rub salt into Newcastle's wounds Elliott was sent off on 90 minutes for fouling Wright-Philips.
It was the defender's second yellow card of the game, following his 38th minute booking for a foul on Drogba.