Both Pompey and their Dutch opposition were playing for little more than pride after neither side had managed to win any of their three previous games and had no chance of reaching the last 32.
But two Peter Crouch goals in three first-half minutes eased the disappointment around Fratton Park on a day when the home fans also learned that key midfielder Lassana Diarra is to be sold to Real Madrid for a reported fee of £20million in January.
Tony Adams made five changes to the side that lost 3-0 to Newcastle United last weekend, with Jermain Defoe left on the bench and Sol Campbell rested from the squad completely.
In an entertaining opening both sides had chances to break the deadlock as Roy Beerens struck the inside of Jamie Ashdown's near post after latching onto a long ball in the opening stages.
Crouch stabbed an effort wide before the England striker hit the crossbar after taking down Marc Wilson's angled pass with a sublime piece of skill only to lift the ball onto the face of the woodwork.
Lively full-back Armand Traore caused havoc down the Heerenveen right and his shot midway through the first half flew just over the top.
But the Wilson and Crouch combination finally prised open the Dutch defence in the 40th minute when another inviting cross from the full-back was headed home from close range by the rangy striker.
Two minutes later it was 2-0 to the home side when Crouch was on hand to knock in the rebound after goalkeeper Brian Vandenbussche had parried Kanu's shot following a trademark mazy run from the Nigerian.
The open nature of the contest continued after the break and Heerenveen substitute Tarik Elyounoussi should have done better than drag a low shot wide of the mark when played clean through.
Portsmouth seemed content to sit on their two-goal lead as the second half progressed and steadily the attacking threat from the visitors reduced.
But there was still time for Hermann Hreidarsson to add a third when the defender rose at the back post to meet Glen Little's cross with a towering header to set the seal on a long-awaited first European win for the south coast club.