Both sides made one change from their previous league games. Leeds brought in Ilia Gruev for Joe Rothwell and Portsmouth introduced Freddie Potts for Isaac Hayden.
The opening minutes of the game were cagey and competitive as both sides wrestled to get control.
Leeds had a penalty appeal early on that was waved away by referee Robert Jones, after Matt Ritchie tried to clear the ball and ended up sending Dan James to the floor as a result.
John Mousinho's side played some encouraging football in the opening half-hour, threatening the Leeds backline on occasions but not really putting together a real chance to test Meslier.
At the other end, five minutes before the break, Portsmouth keeper Schmid was called into action and made a fine double save to deny Manor Solomon and then Joel Piroe from close range.
Leeds started the second half with another huge chance as James broke down the right-hand side and played the ball across to Solomon, who was clear through with only the keeper to beat.
The forward was forced wide by Schmid and cut a pass back to Piroe, but his effort went over the bar, much to the frustration of the Leeds fans and jeers from the home support.
Portsmouth then found the net just after the hour mark. Bishop ran on to Connor Ogilvie's pass over the top and lifted the ball over the onrushing Meslier and off the far post to score.
Fratton Park erupted and shook with the cheers that followed as Bishop rolled up his sleeves and flexed his muscles in celebration.
Leeds responded and looked set to equalise 15 minutes later after Junior Firpo was played through, but he was denied by another fine close-range save from Schmid.
Moments later, Firpo struck the bar from a header to the despair of the travelling fans behind that goal.
Leeds mounted a late charge but Schmid saved his best until last with a spectacular stop from Byram's header deep into stoppage time to preserve the victory.