Alessandro Diamanti scored his third goal in as many games to maintain West Ham's hopes of survival and keep Portsmouth rooted to the bottom of the Barclays Premier League following the 2-0 result.
The Italian struck from the penalty spot at Upton Park midway through the first half of a match short on quality, clear-cut opportunities or reasons to suggest either team deserve to be higher in the table. Radoslav Kovac added the second just before the end.
Both sides were nervous, struggled to keep possession and gave a clear explanation as to why they started the festive period 19th and 20th in the table.
With the tackles flying in, it was no surprise that a mis-timed challenge led to West Ham's 23rd minute opener.
The move started with Julien Faubert's ball forward for Scott Parker, Younes Kaboul failing to clear when he had a chance and Guillermo Franco getting blocked from his route to goal.
It fell invitingly for Jimenez, who looked to be tripped by former Hammers midfielder Hayden Mullins but replays showed that Brown was the culprit.
Either way, Diamanti confidently tucked away the penalty when Probert pointed to the spot.
Portsmouth could have fallen further behind two minutes after the restart when Diamanti's angled drive deflected off Steve Finnan and Asmir Begovic, in goal as David James is still nursing a calf complaint, had to leap across his goal to pull off a fine save. Diamanti also went over with a cheeky 45-yard lob.
Boateng caused the hosts problems and almost embarrassed Herita Ilunga when the Hammers full-back left a ball for Robert Green to collect. Boateng took the ball away from goalkeeper and defender but his finish went wide.
Kovac headed home Jimenez's free-kick a minute from full-time to seal the win.
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