A solitary penalty from Mark Noble after only 24 minutes was enough to give them all three points.
Winston Reid was pulled down in the box leaving Noble to slot low and to the right of goalkeeper Stephen Henderson.
The Hammers were then guilty of missing a number of chances again as they tried to put some daylight between the sides.
Portsmouth went down to ten men early in the second half when David Norris was sent off for an ugly challenge on Winston Reid. Despite the man advantage the Hammers were unable to break down a resolute Pompey defence as were left hanging onto their slim advantage at the final whistle.