The 10-man Royals, who had defender Ellis Martin dismissed on 31 minutes, endured a tough afternoon against the high-flying Hammers.
Lively teenage striker Cam Munn, 18, netted either side of the break with Eddie Hodge's first-half stoppage-time 30-yard stunner and Steve Devlin's thunderous free-kick after the restart completing the scoring.
The visitors could have won by a greater margin had Portchester stopper Brad Snelling not saved Hodge's spot-kick on 32 minutes down low to his left.
The penalty incident saw the Royals reduced to 10-men a minute earlier when Martin tripped Lee Francis in the area.
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For Wallace, it was the first defeat of his interim manager tenure after securing wins over Blackfield & Langley and Bournemouth Poppies in the past two matches.
Portchester need to quickly pick themselves up as they host Baffins Milton Rovers on Tuesday.