Egyptian striker Mido was involved in both Spurs goals and there might have been more but for two outstanding saves from Pompey goalkeeper Sander Westerveld.
Westerveld prevented Jermain Defoe from twice adding to his second-half goal as Portsmouth struggled to make any kind of impact in front of a stunned home crowd.
In contrast Paul Robinson, the Spurs goalkeeper had only one important intervention to make, cutting out a downward header in the 68th minute from Laurent Robert.
Tottenham were ahead in first-half injury time when Mido threatened to finish off a return pass from Defoe, but was beaten to the final touch by Pompey full-back Andy Griffin.
From that moment on there was only going to be one winner and as Tottenham flourished, Portsmouth faded so that they offered little threat.
Portsmouth manager Alain Perrin took off Ivica Mornar at the end of the first half and replaced him with Vincent Pericard, who was making his first appearance after injury since December 2003.
Pericard was no more successful than his team-mates and it was no surprise when Tottenham added a second goal in the 64th minute.
Mido's pass from near the halfway line eluded Andy O'Brien and Defoe raced away, went around the goalkeeper and slotted in from a difficult angle.
Westerveld may have been partly at fault for both Tottenham goals but he showed his quality twice to deny Defoe.
After four minutes Defoe got in a right-foot shot from 15 yards which the goalkeeper blocked to safety with his legs.
Then with 13 minutes to go, Defoe's shot looked destined for the top corner until Westerveld dived to his left to make a spectacular stop.
Mido came off with ten minutes remaining to be replaced by Frederic Kanoute but by then the damage had been done.
Portsmouth almost mustered an injury-time consolation when Collins Mbesuma came off the bench for his debut, one of seven new signings on show, to get in a low shot from 15 yards which Robinson held on his line.
The only drawback for Tottenham were bookings for the impressive Teemu Tainio for a first-half foul and for Andy Reid for a wild lunge at Griffin in the 58th minute.
Tottenham had such an easy afternoon in defence that one of their few scares came when Erik Edman almost turned the ball into his own goal in the 56th minute in attempting to clear a centre from Robert.
Robert did his best to provide some kind of threat with a series of dangerous centres, corners and free-kicks, but he found little response from his new team-mates.
Spurs were delighted to collect the points after Keane was ruled out at the last minute by an ankle injury, but manager Martin Jol need not have worried because the threat of Mido and Defoe was always too much for a hard-pressed Portsmouth defence.
Man of the Match: Mido – The Egyptian forward caused havoc among the Pompey backline to lead his side to a comfortable victory.