The FA Cup party spilled over into the league as Niko Kranjcar's second-half strike earned them all three points at Upton Park.
Victory takes the Blues to a 56 point return for the season, bettering last season's 54 point haul.
It also reduces the gap to four points on Everton in the fifth and final European berth.
Incredibly, it was also Pompey's 14th away win of the campaign.
The first-half proved to be a flat affair with the home side looking the brighter.
But Pompey showed there was no fatigue after their FA Cup exploits at Wembley on Saturday as they upped the ante after the restart.
They served notice of their intent before Kranjcar spun on the edge of the box after 61 minutes from Muntari's pass and buried a fine low drive past Rob Green.
West Ham rarely looked like getting back into the game after the goal as the Blues' rearguard held firm, allowing David James to pick up the team's 21st clean sheet of the season.