Chance were limited in a scrappy affair. Jed Wallace tested Steve Arnold with a fiercely-struck free-kick after 24 minutes, but the Boro goalkeeper clung on well.
The visitors had the ball in the net after 31 minutes when Filipe Morais' raced on to Luke Freeman's ball behind the home defence. However, his effort was ruled out for offside.
Morais was close to breaking the deadlock after 74 minutes when his flicked header from Freeman's cross bounced just wide.
Pompey substitute Adam Webster was lucky to get away with a major blunder after 83 minutes when he blasted the ball against Stevenage's James Dunne on the edge of his own box. The ball flew just over the crossbar.
Webster atoned a minute later when his stunning diving header was well caught by Arnold.
Stevenage's Marcus Haber nodded against the Pompey crossbar with the last action on the match as neither side found the breakthrough.