Jed Wallace opened the scoring for Pompey in the 20th minute and Morecambe never looked like seriously threatening the home side's dominance or getting back into the game.
Connolly's third goal of the season came soon after when he swept home a rebound after a shot from Andy Barcham had been blocked.
Morecambe, who lost first-choice goalkeeper Barry Roche to illness during the warm-up, saw defender Andy Wright sent off in the 38th minute for a second yellow card offence, and the match was soon over as the powerful Agyemang fired home a third.
For Portsmouth it was a first win of the season since being relegated to League Two while Jim 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.
Whittingham said: "I am delighted with our first win and I hope we can push on from here. I have to say we have played well in our previous two league matches without getting the results.
"In the first half everything fell into place but there is no sense of euphoria in the dressing room because the lads felt we should have gone in the second half and got one or two more.
"Our front two of Agyemang and Connolly have a great understanding. They have got five goals between them now but they know they have to keep up that standard because there are players itching to replace them if they fail.
"Barcham was unplayable. He was full of confidence and is proving a real asset already."