He set Pompey on their way into the last 16 with a well-worked opening goal ten minutes before half time.
The England Under-21 international slotted home at the back post after Scunthorpe goalkeeper Tom Evans could only parry a shot from Israeli international Eyal Berkovic.
Taylor doubled Pompey's lead midway through the second half with his second goal of the game - only the left-back's third of the season.
The former Luton star drilled the ball into the bottom left-hand corner after Sheringham had superbly turned substitute Sebastien Schemmel's cross into his path.
Scunthorpe had wasted two glorious opportunities to get themselves back into the match, before Taylor completed his brace.
Steve Torpey should have scored within a minute of the restart, but headed over with only Portsmouth goalkeeper Shaka Hislop to beat after Matt Sparrow had crossed from the right, before Paul Hayes forced a fine save from Hislop just two minutes later.
The Division Three outfit gave their lofty opponents a fright when substitute Andy Parton volleyed them back into the match four minutes from time - his first goal for the club, and just weeks after playing Unibond League football with Harrogate Town.
Pompey defender Dejan Stefanovic failed to deal with a throw in allowing substitute Parton to rifle home with a ferocious left-footed volley from ten yards out.
But Parton's goal proved to be the only ray of sunshine for the travelling Iron fans, as Portsmouth shut up shop to hang on to their victory.
