Chelsea were unimpressive in torrential rain at Fratton Park and the home side had two glorious opportunities to go ahead before Didier Drogba's fine finish settled the match.
Chelsea have 58 points from 28 games and are ahead of Liverpool on goal difference after David Ngog and Yossi Benayoun struck to give Rafa Benitez's side victory at home to Sunderland.
United have two games in hand on both, starting with their trip to struggling Newcastle United on Wednesday when they will be seeking to stretch their winning run in the league to 11.
Fifth-placed Arsenal ended their recent goal famine when Nicklas Bendtner scored twice in a 3-1 victory at bottom club West Bromwich Albion which put them just three points behind Aston Villa in the race for a top-four spot.
Arsenal had drawn their previous four league matches 0-0.
LIVING DANGEROUSLY
Chelsea appear to have rediscovered the art of winning when playing below their best, as they often did in securing back to back titles under Jose Mourinho.
They lived dangerously in the second half and twice Portsmouth went close to taking the lead.
David Nugent was clear on goal but saw his shot well saved by Petr Cech and then a Portsmouth counter-attack led by Peter Crouch ended with Niko Kranjcar shooting narrowly wide.
Drogba struck with a low shot from Jose Bosingwa's cross 12 minutes from time to give Chelsea their fourth consecutive victory by the odd goal since Guus Hiddink replaced Luiz Felipe Scolari as manager.
Before the game Portsmouth confirmed that Paul Hart would remain as manager until the end of the season, having taken over from sacked Tony Adams on a caretaker basis in February.
Liverpool went ahead seven minutes after the break against Sunderland when Steven Gerrard headed the ball across goal for Ngog to tap in his first Premier League goal.
The home side doubled their lead when keeper Marton Fulop made a meal of saving an overhead kick from Ngog and Benayoun, who scored the winner in the Champions League victory at Real Madrid last week, tucked in the rebound.
