The transfer target for London rivals Spurs struck twice in the last 20 minutes to seal victory for Gianfranco Zola's team.
Tricky striker Bellamy deserved his two goals as sorry Portsmouth were put to the sword. Carlton Cole also netted as did Jack Collison as Pompey fell apart.
Portsmouth have only kept one clean sheet in the league since Adams was named boss and they had an early scare.
Bellamy was brought down just outside the box by Sol Campbell's clumsy challenge. The Welshman put his free-kick over the wall but it also went well over the bar after failing to dip.
However, Portsmouth took the lead in the eighth minute when left-back Nadir Belhadj capped off a superb move with the opening goal.
England international Peter Crouch nodded a cross to strike partner Jermain Defoe who pulled the ball back for Belhadj to fire home from 15 yards.
Both sides looked great going forward but shaky at the back and West Ham deservedly equalised after 20 minutes.
Scott Parker took a quick free-kick to Cole who crossed from the byline to Collison. The midfielder fired the ball through two defenders with David James unsighted.
West Ham then should have taken the lead after a comedy of errors in the Pompey defence. Glen Little attempted to pass the ball back to James but Bellamy nipped in and found Mark Noble.
The midfielder curled the ball goalwards but Sylvain Distin got back to head clear.
Pompey wasted an opportunity to take the lead two minutes before the break when Defoe missed a penalty against his former club. Referee Steve Bennett pointed to the spot after Lucas Neill had pushed Crouch over but Defoe fired wide of the left-hand post.
Bellamy set up Cole who fired the Hammers into a 67th minute lead and they made it 3-1 three minutes later when Bellamy smashed home his third of the season.
The striker added a fourth with seven minutes left as Pompey were put to the sword by a rampant West Ham side.
Adams only has two wins in 11 games since taking over from Harry Redknapp and the pressure is now on him as his side slide down the table.