A late Liam Lawrence goal set up a tense finale at Fratton Park following Richard Hughes’ straight red card but Leicester held on.
Both clubs have struggled so far in the npower Championship but Paulo Sousa’s side have saved their best performances for this competition and it proved to be the case once more.
Leicester started brightly and Dyer had already forced Jamie Ashdown into a parrying save when Morrison turned the ball home from close range after three minutes.
Dyer, the architect for the first goal, then got on the scoresheet himself two minutes before half-time with a low, left-footed shot from the edge of the box.
The two goalscorers for Leicester, along with Andy King, were the only survivors from the side that started the league defeat to QPR at the weekend as Sousa made eight changes.
Portsmouth boss Steve Cotterill recalled Ibrahima Sonko, Hughes, Matt Ritchie and Nwankwo Kanu in four changes from the team that lost at Sheffield United.
Kanu came close to cancelling out Morrison’s opening goal in the fourth minute when his first-time shot from 12 yards went narrowly wide.
Steve Howard had two opportunities to extend Leicester’s lead before the 10-minute mark but the burly striker failed to hit the target on both occasions.
It almost proved costly as only a fine save by the legs of Conrad Logan to deny Lawrence kept the Foxes ahead after 13 minutes.
Paul Gallagher struck a 12-yard shot against the crossbar midway through the first half before Ashdown fumbled a long-range effort by Joao Moreno as Leicester threatened a second goal.
It arrived in the 43rd minute when Dyer collected King’s pass and beat Ashdown with an angled shot into the bottom corner.
It may have been a different game had either Kanu or David Nugent made the most of their opportunities to halve Pompey’s deficit before the break. Kanu headed wide while Nugent at least forced Logan into a parrying save with an effort from around the penalty spot.
By comparison, the second half was less eventful. Nugent worked Logan again 10 minutes after the restart, this time from the edge of the box, before Hughes was needlessly sent off for dissent after 66 minutes.
Portsmouth’s numerical disadvantage did not deter them, and Lawrence forced Logan to push away another shot in the 75th minute.
With eight minutes remaining, Pompey were given a lifeline. Logan saved Joel Ward’s effort and Lawrence drilled a low shot into the net on the follow up. However, Cotterill’s charges could not find an equaliser.