Two classy finishes from substitutes Eidur Gudjohnsen and Arjen Robben put Chelsea in the Carling Cup last eight.
Icelandic striker Gudjohnsen arrowed a shot past Shay Given in the first period of extra time, just five minutes after coming off the bench.
Robben's goal was even better as he beat three players before slipping the ball past Given into the corner.
Marshalled by John Terry the Chelsea defence allowed Newcastle few chances, though Laurent Robert twice went close.
Gudjohnsen took his goal superbly, allowing a Robben pass to run across him, providing a little bit of space, before he powered a shot past Given, the ball going in off the post.
In the second period of extra-time Robben claimed his second goal in two games, running almost half the length of the pitch, in the process beating three Newcastle defenders and then side-footing home.
Until Gudjohnsen's arrival Chelsea had played with just one striker, the Serbian Mateja Kezman, though both Damien Duff and Joe Cole always tried to get forward and support.
Kezman has managed just one goal in 15 appearances since joining Chelsea from PSV Eindhoven, but he almost doubled that tally in the second minute.
The Chelsea striker pounced on Andy O'Brien's casual pass and slipped the ball past Shay Given, but from a tight angle Kezman was unable to turn his shot home.
That proved to be Chelsea's best effort in the first-half, though Glen Johnson selfishly shot from a difficult angle, much to the annoyance of Duff and Kezman, who were waiting in the box.
Not that Newcastle managed to create too many openings in a fiesty opening 45 minutes that saw Cole, Tiago, Johnson and Nicky Butt all booked.
Newcastle's best chance was an Olivier Bernard shot that Cudicini touched past the post.
Bernard had released by a pass from Laurent Robert, who also troubled Cudicini with an inswinging corner.
Soon after the restart Robert weaved his way into the Chelsea box, only for his shot to be blocked by Scott Parker's last-ditch tackle.
Late in the game a swerving Robert free-kick drew a superb reaction save from Cudicini, who fisted the ball away.
On 62 minutes another home defensive lapse - this time from Titus Bramble - nearly allowed Cole to escape, but the Newcastle defender recovered quickly.
Two minutes later Cole and Kezman combined to free Tiago, only for the former Benfica midfielder to miss with just Given to beat.
Given also had to rush out of his box to hack the ball clear as Arjen Robben threatened.
When the game moved into extra-time Chelsea took control and the goals from Gudjohnsen and Robben mean Mourinho's side have won their last seven games in a row.
Newcastle: Given, O'Brien, Bramble, Johnsen,
Bernard (Hughes 118), Bellamy, Butt (Dyer 45), Jenas, Robert,
Shearer, Kluivert (Ameobi 105).
Subs Not Used: Harper, Bowyer.
Chelsea: Cudicini, Johnson, Terry, Gallas, Bridge,
Paulo Ferreira, Tiago, Parker (Gudjohnsen 96),
Duff (Robben 63), Kezman, Cole (Lampard 66).
Subs Not Used: Cech, Huth.
Booked: Tiago, Johnson, Cole.
Goals: Gudjohnsen 100, Robben 112.
After Extra Time.
Ref: S Bennett (Kent).