Goals from Pompey old-boys Peter Crouch and Niko Kranjcar secured a routine victory for Harry Redknapp's men, who continued their quest for Champions League football in ruthless style.
Spurs are now five points clear in fourth and have just seven matches left to clinch a place in Europe's premier competition - and a fifth straight victory in the league has given them the best chance they can hope for.
Time is running out for bottom club Pompey, but they began with a tenacity that seemed to stun Spurs - Anthony Vanden Borre came agonisingly close to opening the scoring on 18 minutes, but Heurelho Gomes came out on top in their one-on-one battle.
Vanden Borre was made to pay for his profligacy as Crouch stooped to nod Gareth Bale's excellent cross past David James on 27 minutes.
James was at fault for the opener and could only watch as first Tom Huddlestone smacked the crossbar, before Crouch cracked the post.
It wasn't long before Kranjcar got in on the act as the former Pompey midfielder tucked home from close range after the visitors failed to clear Luka Modric's low shot.
Avram Grant's men should have reduced their arrears just before half-time, but Michael Brown shot straight at Gomes when it looked easier to score.
Pompey boss Grant never looks like the most cheerful of managers and his hangdog expression became even more sinister when Herman Hreidarsson was taken from the field with what looked like a serious ankle injury.
He needed oxygen as he left the pitch, with his FA Cup semi-final hopes seemingly dashed.
If Portsmouth are to have any chance against Spurs at Wembley, they will need to fight a lot more than they did at White Hart Lane. Richard Hughes flashed a drive wide on 60 minutes, but that was as good as it got.
In fairness, they did impose themselves on the hosts in the second half, but the lack of a cutting edge in front of goal was there for all to see.
Crouch went close late on but fired wide, but it mattered little as Spurs had this one won in the first half.