Jed Wallace opened the scoring for Pompey in the 20th minute and the Shrimps never looked like seriously threatening the home side's dominance or getting back into the game.
Morecambe, who lost first-choice goalkeeper Barry Roche to illness during the warm-up, saw Wright sent off in the 38th minute for a second yellow card offence, and the match was soon over as the powerful Patrick Agyemang fired home a third.
For Portsmouth it was a first win of the season since being relegated to League Two while Bentley's Morecambe are still looking for their maiden success after being overwhelmed in the opening 45 minutes when Pompey were at their rampant best.
"I think the red card was fair. Andy gave the referee no choice but to send him off, which is very disappointing," he said.
"He gave away three silly fouls, diving in when he need not have done and that obviously did nothing for the team at that stage.
"Blink and we were 3-0 down, that is how quick it was. The game was dead and buried by half-time but at least we had a go in the second half, even if the fear factor had long gone. There is no fear when you are 3-0 down.
"People say to me about playing Newcastle in the League Cup, but ithad no effect here and I, for one, am not even thinking about Newcastle. It is our league form which is the worry.
"We only have a small squad and some of the lads are coming back to fitness but there was no point in rushing them back before they were ready."