Ramires scored twice in two minutes in the closing stages as Chelsea booked a place in the FA Cup fourth round.
Andre Villas-Boas' side struggled for a cutting edge against Championship side Portsmouth at Stamford Bridge but took the lead when Juan Mata swept in from close range just after half-time.
Ramires poked in at the far post, and then finished off a counter-attack.
Frank Lampard added a fourth from the edge of the area late on to give the scoreline a flattering gloss.
Ramires is hardly known as a prolific goalscorer, but his late double takes his tally to eight for the season - making him the club's third top-scorer.
It was the first time Chelsea have managed four goals since their 5-0 victory over Genk in the Champions League in October.
But it was not a reflection of the way they played and there was yet more frustration for Fernando Torres.
With Didier Drogba away at the Africa Cup of Nations with Ivory Coast for much of January, Torres looks set to get a run in the Chelsea side.
But, looking for a first goal since October, he was starved of service throughout and only threatened on one occasion, when he did well to force a save from Stephen Henderson with a header after being picked out by Florent Malouda on the edge of the area.
Mata's sixth goal since joining in a £23.5m deal from Valencia in the summer set the Blues on their way to victory.
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Ramires' tally of eight goals has already beaten his previous best (seven goals for Cruzeiro in 2008/09) for an entire campaign.
But against a team struggling in the second tier, Chelsea would have been expected to trouble Henderson far more than they did before a flurry of three goals in eight minutes late on.
Dave Kitson went close to opening the scoring with a drive that flashed just wide of goal with less than 30 seconds gone.
Aaron Mokoena, one of three survivors from the Portsmouth team that was beaten 1-0 by Chelsea in the final in 2010, missed with a header from a Liam Lawrence corner.
After failing to turn their possession into any more chances in a forgettable first half, the Blues grabbed the lead just two minutes after the interval.
Malouda, who was making his first start since November, embarked on a powerful run down the left flank and his low cross was calmly finished from close range by Mata.
But Portsmouth had several chances to pull level in a scramble after David Luiz gave the ball away.
Petr Cech saved from Marko Futacs and John Terry, who required treatment after colliding with the post, blocked from Ricardo Rocha before Cech denied Futacs once again.
Chelsea looked likely to limp to victory before Mata's cross flew over Torres and Jason Pearce for Ramires to stab in with four minutes left.
Two minutes later, the hosts broke swiftly and Ramires touched in from a Torres assist.
And three minutes into stoppage time, Ramires contributed the final pass before Lampard drove in from the edge of the area for his tenth goal of the season.
Chelsea assistant manager Roberto Di Matteo:
"I thought it was a very good all-round performance. Portsmouth made it very hard, especially in the first 45 minutes, and it is always difficult to break an opponent down and find a space with so many players.
"It was just a matter of scoring the first goal and we were always confident we were going to be able to do that.
"In the second half we got further forward and secured the win. It is a competition we would like to win and today we have gone a step further towards the target."
Portsmouth manager Michael Appleton:
"Conceding after two or three minutes of the second half does not help matters, especially after a good first-half performance.
"I thought we got back into the game and you could sense there was a bit of nervousness before the end when they got their second goal.
"I think the performance was a credit to the boys but that is why Chelsea are where they are and we're a Championship club."
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