Pompey saw off a tricky Shrewsbury side to start the season with three successive league wins for just the second time in 33 years.
Ryan Tunnicliffe netted the only goal of the game with just 120 seconds on the clock after swapping passes with Marcus Harness.
But Danny Cowley's men did not have it all their own way and Gavin Bauznu made a fine late save to deny Aaron Pierre.
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