Demba Ba notched up his first goals for the Blues as his new side thrashed Southampton 5-1 in the FA Cup at St Mary's.
Further goals from Victor Moses, Branislav Ivanovic and Frank Lampard ensured that there would be no shock at St Mary's.
However the home side did have the temerity to open the scoring on 18 minutes through Jay Rodriguez.
Both sides started with strong sides, with the visitors' Demba Ba starting ahead of Fernando Torres dropped to the bench for the first time this season.
As expected , Saints started cautiously, allowing the Blues the greater volume of possession, while defending deep.
Chelsea-Mad can happily report that on 16 minutes, as sure as day follows night, chants of 'One Di Matteo' rang loud and clear from the 4,500 travelling Chelsea fans . They simply will not allow the Chelsea hierarchy to forget how unhappy they are at the sacking of their
Champions League winning boss, especially to be replaced by Rafa Benietz.
With what looked like a snoozefest developing, the home side decided to go on an attack.
Jason Puncheon sliced open the Chelsea rearguard, laying the ball into the path of Jay Rodriguez, who outpaced Gary Cahill and clipped the ball from just inside the Chelsea area over Ross Turnbull and into the net.
Eden Hazard tried a speculative shot two minutes later, his right-footed effort zipping past Artur Boruc's left upright.
But the Blues levelled the score on 35 minutes with a fine breakaway of their own, Hazard of the left, cut inside, fed the ball to Mata. His effort was goal-bound before Ba popped up in front of Steven Davis to tap home his first goal since his move on Friday from Newcastle United.
Cesar Azpilicueta then showed he has a fine shot, letting fly a fierce right-footer. The ball bounced in front of Boruc and the Polish goalkeeper had to take a second grasp of the ball to get it under control.
But the Blues soon made their dominance tell and struck their second deep into added time.
Captain Ashley Cole, on the edge of the Saints penalty area, cut the ball back to Victor Moses who dispatched the ball past Boruc with a fine left-footed half volley.
It took just five minutes of the second half to, all but ensure the Blues entry into the 4th round, when centre-back Branislav Ivanovic struck home the simplest of headers from close range after Mata sent in the perfect clipped left-footer.
Goal number four came 10 minutes lat and it was a move which was started by Ba and ended with the Senegal striker stroking home from six-yards.
picking the ball up in midfield, Ba passed to Ramires. The Brazil midfielder caressed the ball across to Hazard. Taking one touch, the Belgium midfielder, on the apex on the right of the Saints area, slid the ball into the six-yard box when Ba was on hand to ram home past Boruc.
Frank Lampard entered the fray on 65 minutes for Branislav Ivanovic.
Ross Turnbull, in for the injured Petr Cech produced a double save with 20 minutes to go, firstly thwarting substitute Steve De Ridder and then quickly blocking a shot by Rodriguez.
Lampard had a trademark daisy cutter well held by Boruc but the goalkeeper could do nothing about stopping Lampard's next effort a penalty.
The midfielder needed one more strike to equal club legend Kerry Dixon's total of 193 goals. Frank Lampard got his chance with seven minutes to go when Maya Yoshida arm got in the way of Lampard attempted chip.
Up stepped the midfielder and dispatched the ball into the net with consummate ease.
News that Chelsea are in talks with Lampard regarding clarity on a new contract will be welcome news for e Chelsea faithful.
Whether that translates into a firm offer is still open to speculation.
Should this be Lampard's last season, then he has until May to get his total up to 203 and become Chelsea's all-time goal-scoring record holder - beating current holder Bobby Tambling.
The game petered out with the Blues safely into the next round.
Next up for Chelsea is the semi-final of the Capital Cup when they face Swansea City.
The first leg is at home on Wednesday.
Teams: Chelsea - Turnbull, Ivanovic, Cole, Luiz, Ramires, Mata, Moses, Hazard, Cahill, Azpilicueta, Ba
Subs - Hilario, Lampard, Torres, Oscar, Ferreira, Marin, Bertrand
Southampton - Boric, Yoshida, Schneiderlin, Fonte, Davis, Rodriguez, Ward-Prowse, Cork, Do Prado, Shaw, Puncheon
Subs -Davis, Hooiveld, Lambert, Lee, Mayuka, Reeves, De Ridder
Referee Mike Dean