Two goals from Didier Drogba and one by Robben keep the Blues top of the league and 11 points clear of second-placed Manchester United.
The three goals came in a 23-minute spell midway through the first half which destroyed Portsmouth's futile resistance.
And it was the flying Dutchman, who is 21 on Sunday, who did most of the damage.
After a tough opening ten-minute spell which saw Portsmouth mount a concerted challenge on goal, Chelsea suddenly found their expressive form.
It started with a Drogba right footer, which, while hopelessly wide, served as a precursor of things to come.
A minute later Robben weaved his magic on the right. He sailed past two defenders before cutting back a ball from the byline.
Drogba, alert to the possibility of a simple goal, backed away from his marker, found an inch of space and waited.
It came of course because Robben is an exceptional talent and he laid the ball perfectly at the feet of the Ivory Coast striker, ahead of the despairing lunge of goalkeeper Jaime Ashdown.
Drogba tapped the ball home with his right foot from five yards out - simplicity itself.
It was six minutes before the second goal came - and it was a goal that typified Chelsea's performances this season.
After a period of keep ball, Chelsea punched forward. The ball fell to Drogba who fed the ball to Frank Lampard.
England's best player of 2004 produced an inch-perfect ball that bisected the Portsmouth defence.
The in-coming Robben raced into the penalty area, collected the ball and skipped past Ashdown.
It looked as if the Dutchman might have taken the ball out of play, but so quick is he, that he managed to cut a right footer into the net from an acute angle.
Stamford Bridge erupted as the Chelsea fans realised that this was not going to be a banana skin match.
But, just as they were looking towards an avalanche of goals, Chelsea almost gifted the south coast side a lifeline.
Lampard in midfield made a limp attempt to play the ball back to John Terry. It was short and was expertly intercepted by striker Yakubu.
The front man arrowed towards goal unchallenged and when Chelsea goalkeeper Petr Cech came out to meet the challenge, he suddenly stopped.
It appeared that with the goal at his mercy, all Yakubu had to do was to slide the ball home.
But the Nigerian striker conspired to miss the best chance of the match for Portsmouth - by screwing the ball wide of Cech, but more importantly wide of his right upright.
It was just the fillip Chelsea needed because two minutes later the game was over.
Robben, not for the first time, was upended just outside the penalty area, wide on the right.
Up stepped Drogba and Damien Duff. Who was going to take the free-kick? Certainly Ashdown didn't know as he paced along his line. But Chelsea had the move all worked out.
Duff ran over the ball, leaving Drogba free to strike a beautifully right footer over the static Portsmouth wall.
Ashdown did well to anticipate the direction of the curler, and even managed to get his fingertips to the ball, but the sheer power defeated him and the ball bellowed the back of the netting.
Three nil before half-time and one expected more goals.
But Jose Mourinho decided to contain the match in the second half and the game died a death as a spectacle.
Not good for the paying public, but Mourinho is ultra professional and won the game with ease. It seems the title will be coming to Stamford Bridge this season.
MAN OF THE MATCH: John Terry (Chelsea) – Solid as a rock at the back as the Blues strolled to yet another victory.