The victory also gave manager Harry Redknapp revenge for his surprise defeat at Field Mill last year, when his Southampton side were one of the Stags' scalps.
But brave Mansfield at least had the satisfaction of becoming the first side to score against Portsmouth this season when substitute Danny Reet struck a late goal to cap a fine second-half fightback.
Pompey, who made ten changes from Saturday's win at Charlton, still fielded a strong side full of internationals - including debutants Andrew Cole, Croatian midfielder Niko Kranjcar and on-loan Benfica star Manuel Fernandes.
And it took Fernandes just five minutes to make his mark, smashing a 30-yard drive into the top corner with only his second touch of the ball for the Premiership side.
The goal settled any Pompey nerves, but the Stags still created chances to level. Richie Barker just failed to touch in Matt Hamshaw's deep corner and then headed straight at the keeper from another flag kick.
Mansfield, beaten twice in the previous week on their travels and with just two wins from 15 League games, belied their position 82 league places below Portsmouth to go close again through Stephen Dawson and Hamshaw.
But their hopes of a cup upset ended 12 minutes before half-time when slack marking at a short corner allowed Matt Taylor - the only player not to be rested from Saturday - to rifle a low 20-yard drive past motionless keeper Jason White.
Cole then twice went close to stretching the visitors' lead with a glancing header and a neat turn and shot at the near post.
Mansfield launched a spirited fightback at the start of the second half and Chris Beardsley should have become the first player to score against Portsmouth this season, but his close-range header lacked power and Dean Kiely saved on the line.
In the 58th minute Beardsley, again fed by Barker, somehow missed the target from less than six yards as the League Two side piled on the pressure.
Then, as Pompey struggled to get out of their own half, Giles Coke tested the keeper from long range and Hamshaw fired narrowly wide after a slip from Taylor gave him a clear run on goal.
Mansfield finally gained reward for their second-half recovery when Reet raced clear onto Richard Duffy's poor back pass and rolled a shot past the stranded Kiely.
But it was too little, too late for the underdogs.