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The 20-year-old cut inside Georges Santos before firing inside the far post, but ten minutes later he missed a similar chance, firing over the bar from Paul Merson's pass.
Pompey dominated the rest of the first half. A Merson free-kick curled narrowly wide of Danny Coyne's goal on 31 minutes and five minutes later debutant Tim Sherwood had an eight-yard shot deflected over the bar.
Harry Redknapp's side continued to dominate after the break, but did not score their second until Grimsby defender Simon Ford put past his own goalkeeper on 74 minutes.
Ford deflected Matthew Taylor's cross-come-shot and in injury time Nigel Quashie sealed the win when he netted from 12 yards following Merson's angled ball from near the halfway line.
Portsmouth goalkeeper Shaka Hislop was only tested once when Darren Mansaram's 83rd minute header forced him to concede a corner.
Grimsby manager Paul Groves said: "It was disappointing because all their goals came when we had the ball.
"We lost control of it and got punished for not taking care of the ball.
"We had a spell in the second half when we pegged them back a bit and created one or two opportunities but against sides like Portsmouth you have to take them."