Connolly's goal came in the 26th minute, snapping up a rebound after a shot from Andy Barcham had been blocked.
Morecambe's cause was not helped 10 minutes later when defender Andy Wright, who had been cautioned earlier, earned a second yellow card to receive his marching orders.
Patrick Agyemang then made the game safe for Pompey soon after when his shot from Connolly's involvement went in off a post.
The match, already comfortably won by the rampant home side, failed to live up to the excitement of the first half after the break.
The nearest either side came to a goal was in the 62nd minute when a shot from Morecambe's Tony Diagne was held at the second attempt by Pompey goalkeeper Phil Smith.