Hermann Hreidarsson and Kanu both had chances to put Portsmouth ahead within 15 minutes of the start, but Hreidarsson was just wide with a close-range header and Neil Alexander was alert to Kanu's timid effort.
Pompey, defending high up the field, pegged Ipswich into their own half and the home side's frustration flared up with Trotter's dismissal.
The midfielder mis-timed his sliding tackle on Portuguese international Mendes and to the 19-year-old's astonishment - and the Portman Road faithful's - referee Mark Halsey showed a straight red when a yellow would have sufficed.
Ipswich rallied, with Billy Clarke and Denny Haynes impressing, but were unable to breach Portsmouth's defence as the score remained goalless at half-time.
The lively Haynes looked to have given the home side the lead within minutes of the re-start but David James dived low to his right to keep out Haynes's 25-yard effort.
Moments later, and against the run of play, Nugent gave the visitors the lead.
It was Nugent's first goal since the end of September in what has been a troubled season for the striker since his £6m arrival from Preston in the summer.
But he came close to doubling the advatange on the hour, only for his volley to hit the crossbar.
Ten minutes before the final whistle, John Utaka had the goal at his mercy to cement victory but the striker shot wide when it was easier to score.
Ipswich had a chance to make Utaka pay for his profligacy but James again acrobatically saved a menacing Haynes long-range effort.
The home side bombarded Portsmouth's penalty box to set up a grandstand finish but the Pompey defence remained imperious.
Ipswich:
Alexander, Wright, Wilnis, Bruce, Sito (Naylor 89), Haynes, Williams (Lee 79), Garvan, Trotter, Counago, Clarke (Peters 59).
Subs Not Used: Supple, Miller.
Sent Off:
Trotter (24).
Booked:
Counago, Lee.
Portsmouth:
James, Johnson, Campbell, Distin, Hreidarsson, Diop, Pedro Mendes (Nugent 46), Mvuemba, Utaka, Kranjcar, Kanu.
Subs Not Used: Lauren, Traore, Pamarot, Begovic.
Booked:
Hreidarsson.
Goals:
Nugent 51.
Att:
23,446
Ref:
Mark Halsey (Lancashire).
BBC Sport Player Rater man of the match:
Portsmouth's David Nugent 8.50 (on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.