Scotland midfielder Fletcher slid in with Sol Campbell for Patrice Evra's cross and the ball bounced kindly off his knee, before Sylvain Distin turned the ball into his own net from a yard out.
The victory could not cover up United's desperate need to recruit Tottenham striker Dimitar Berbatov as the European Cup holders produced another toothless attacking display.
Senegal midfielder Papa Bouba Diop came close to giving Pompey a dream start when he shot inches wide of Edwin Van der Sar's right-hand post with only ten seconds on the clock.
Paul Scholes forced David James into his first meaningful save in the 19th minute with a swerving 30-yard piledriver, which forced the veteran goalkeeper to dive full length to his left to keep it out.
Peter Crouch should have put Portsmouth in front six minutes later after being presented with a golden chance by some comical United defending.
Scholes inexplicably smashed a 40-yard back pass straight into touch and a quick throw-in set Jermain Defoe away down the left.
Defoe's cross bounced off Evra to the feet of Nemanja Vidic, who slipped in front of Crouch, but the former Liverpool striker shot straight into the chest of United goalkeeper Van der Sar.
United were given another let-off from the resulting corner when Younes Kaboul was left totally unmarked only to head wide from Sean Davis' centre.
Kaboul was made to pay as Fletcher opened the scoring soon after.
Wayne Rooney was furious with himself for not extending United's lead in the 41st minute.
Scholes and Anderson linked up brilliantly down the right before the Brazilian pulled the ball back for Rooney, who dragged his shot wide from 16 yards with only James to beat.
Portsmouth had beaten United in three of the pair's five Premier League meetings at Fratton Park, but never looked likely to extend that proud record as their expensively assembled front two of Crouch and Defoe were stifled by Rio Ferdinand and Vidic.
After the interval Pompey rarely threatened, although winger Jerome Thomas tested Van der Sar with a stinging drive on the hour mark.
The Dutch keeper was also on hand to divert away a swerving Bouba Diop effort as United comfortably held out for a valuable three points.