Chelsea moved back to the top of the Premiership as two of their under-fire summer signings, Andriy Shevchenko and Michael Ballack, scored a goal apiece.
Shevchenko celebrates scoring Chelsea's opener
Previously goal-shy striker Shevchenko gave the Blues the breakthrough their dominance deserved on 55 minutes when he slotted in Frank Lampard's cutback.
And two minutes later Ballack, who had been off-key, nodded Didier Drogba's headed pass into the top corner.
Benjani pulled one back for Portsmouth, converting after a goalmouth scramble.
That was totally against the run of play and left the scoreline a poor reflection of the match, which Chelsea dominated from start to finish.
An inspired David James in the Pompey goal repeatedly kept Chelsea at bay and spared his side a thrashing.
The majority of those stops came in the first half as Chelsea's fluid play and interchanging left the usually sound Pompey defence bewildered.
Arjen Robben, restored to the line-up in place of Claude Makelele, almost opened the scoring when he raced clear on goal, but James spread himself superbly to deflect the Dutchman's chip wide.
And James was equally excellent when he dived full length to turn away a curling shot from Shevchenko.
Portsmouth had started as though they might make a game of it, and with Kanu in-form up front must have felt there was a chance they could upset the champions.
But Michael Essien had clearly identified the threat of the Premiership's joint top-scorer and sent in a typically robust challenge on Kanu early on.
Perhaps the lanky Nigerian did not fancy it much after that as he was fairly quiet as Pompey were forced on the back foot and he did not come out for the second half.
There was, however, no doubt that Chelsea fancied it - and Robben in particular.
But each time the winger jinked his way into space and unleashed a shot, James was there to repel the effort.
That all changed after the break, when Robben turned provider instead.
And it was his centre into the box which Shevchenko latched onto and finally beat James, albeit with help from a deflection off Sol Campbell's toe.
Relief was evident, both for Shevchenko - who was booked for his celebrations - and for Chelsea.
And that soon turned into a more comfortable feeling for the hosts as Ballack timed his run into the box to connect with Drogba's clever header across goal and put Chelsea two up.
It was Ballack's first Premiership goal for the Blues, and he celebrated as hard as Shevchenko had - and was also cautioned for it.
The German was later denied a second by another superb save from James, who dived to his right to smother a fierce volley.
But before that, Portsmouth had threatened to make the last 20 minutes uneasy for Chelsea as Benjani tucked in from close-range.
A nervous finale did not materialise though as Chelsea's superiority told.
And James was forced into another fine stop late on, tipping Drogba's lashed effort over the bar.
Chelsea boss Jose Mourinho:
"It was difficult because we played a tough game in midweek and Portsmouth are a good team.
"The first moments were difficult and Portsmouth were the better team.
"But we created a lot of chances after that and David James was outstanding. We should have killed the game but we did not. But a victory is a victory."
Portsmouth boss Harry Redknapp:
"David James has been fantastic - he's like an 18-year-old in training.
"He should still be knocking on the England door. Paul Robinson is a good goalkeeper but if you look at the other lads, they are all out on loan.
"He'll play for another five or six years in my opinion."
Chelsea: Hilario, Paulo Ferreira, Ricardo Carvalho, Terry, Ashley Cole, Essien, Lampard, Ballack (Boulahrouz 90), Robben (Joe Cole 66), Shevchenko (Makelele 76), Drogba.
Subs Not Used: Makaba-Makalamby, Wright-Phillips.
Booked: Shevchenko, Ballack, Joe Cole.
Goals: Shevchenko 55, Ballack 57.
Portsmouth: James, Pamarot, Primus, Campbell, Taylor, O'Neil, Pedro Mendes (Thompson 83), Fernandes (Cole 58), Kranjcar, Mwaruwari, Kanu (Davis 46).
Subs Not Used: Kiely, O'Brien.
Booked: Pamarot, Pedro Mendes.
Goals: Mwaruwari 69.
Ref: M Clattenburg (Co Durham).