Niko Kranjcar drilled in a 61st-minute winner to maintain Portsmouth's momentum at the expense of Harry Redknapp's former club West Ham.
It was the FA Cup finalists' ninth win in its past 11 games and its 21st clean sheet of the season.
Pompey have never lost to the Hammers since promotion to the Barclays Premier League in 2002 and their victory condemned their Upton Park hosts to a fifth loss in their last seven.
It also took Redknapp's team within four points of fifth-placed Everton and it could still grab a UEFA Cup place without having to rely on beating Cardiff at Wembley.
The omens for that did not look too bright at the start, though, and the first half will not live long in the memory.
Portsmouth, starting without Kanu, Jermain Defoe and Milan Baros, showed little in attack until the closing minutes of the first 45 as David Nugent toiled against Anton Ferdinand and Jonathan Spector.
It was also short in midfield, with artful French playmaker Lassana Diarra out resting a sore hamstring, and their lack of craft allowed west Ham to constantly feed Dean Ashton and the returning Bobby Zamora.
Zamora wasted a great opening in the ninth minute when he ran clear down the left but failed to find a team-mate with his low pull-back, giving Hermann Hreidarsson the chance to clear.
But he and Ashton continued to cause Portsmouth problems and Pompey's defending looked fairly desperate in the opening 20 minutes.
A strange lethargy seemed to overtake West Ham early in the second half after a couple of through-passes failed to find their marks.
Pompey sensed the frustration creeping in and Kranjcar almost put them ahead after 54 minutes when Nugent's square pass set him up for a strike from 20 yards which sizzled just over the bar.
But the Croat's shoot-on-sight policy paid off just after the hour with a classic strike.
English Premier League
West Ham United 0
Portsmouth 1
(Kranjcar 61)