Pompey gave everything in a determined first- half performance but there was no denying Chelsea were the stronger side in the second and deserved their 15th win of the league season.
The two-goal margin flattered Jose Mourinho's table-toppers but there was no denying they deserved their victory.
Chelsea could have won more comfortably if it had it not been for goalkeeper Shaka Hislop who made three outstanding saves.
Hislop kept out a second minute shot from Didier Drogba and then denied the same player after 58 minutes.
A header from Glen Johnson was cleared from the line after 62 minutes and Hislop was again Pompey's saviour in the 70th minute to keep out a close-range effort from substitute Eidur Gudjohnsen.
In the end a goal had to come and it did in the 79th minute.
Dutchman Arjen Robben finished off a five-man move with a deflected left-foot shot past Hislop.
Robben was booked for taking off his shirt in celebration but the goal left Pompey feeling naked and they offered little late resistance.
Even so, Chelsea had to wait until injury time when Gudjohnsen set up a shooting chance for another substitute, Joe Cole, whose left-foot shot gave Hislop no chance.
Chelsea also had Paulo Ferreira booked for a foul and Frank Lampard for kicking the ball away late in the match after a free-kick had been awarded against him.
At the final whistle, Mourinho was quickly on to the pitch to greet each one of his team as they came off the field in triumph, leaving Arsenal and other Championship contenders with plenty of work to do over the second half of the season if they are to catch them.
Portsmouth can look back with pride on a plucky first-half performance in which they had plenty of possession but not much to show for it.
The nearest they came to scoring was in the 20th minute when a swerving shot from Nigel Quashie from 25 yards was acrobatically tipped over the bar by giant goalkeeper Petr Cech.
However, the victory represented Chelsea's 20th clean sheet in all competitions this season and since their only defeat in the Premiership against Manchester City in October, they have collected a staggering 29 points out of a possible 33.