In an uninspiring first half, Stanley stopper Marcus Bettinelli was given a massive reprieve after 23 minutes when he spilled Daniel Alfei's cross from the right under pressure from Pompey defender Ben Chorley.
The ball fell to an unmarked Michael Drennan but he blazed a glorious chance to open the scoring wide.
Portsmouth flew out of the blocks after the break and Jervis fired them ahead just three minutes into the second half when he cut inside from the left and drove a low shot to Bettinelli's right-hand side.
Accrington gave their 61 fans in attendance little to get excited about. A Peter Murphy header forced Portsmouth goalkeeper Trevor Carson to make a comfortable stop after 62 minutes.
Pompey's Ricky Holmes picked out an unmarked Romain Padovani in the Stanley box a minute later, but he lashed his shot wide of the post.
Alfei's 30-yard shot was turned on to the Accrington crossbar by Bettinelli after 89 minutes as Pompey easily sealed a second straight home win.